%R 1998LRR.....1....3R
%A Reula, Oscar A.
%F AA(Universidad Nacional de Córdoba, FaMAF, Ciudad Universitaria, 5000 Córdoba, Argentina)
%J Living Reviews in Relativity, vol. 1, no. 3
%D 01/1998
%T Hyperbolic Methods for Einstein's Equations
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-1998-3
%I HTML: http://www.livingreviews.org/lrr-1998-3; PDF: http://relativity.livingreviews.org/Articles/lrr-1998-3/download/lrr-1998-3Color.pdf; DOI: 10.1007/lrr-1998-3
%K initial value problem, evolution equations, harmonic gauge, initial boundary value problem, mixed systems, symmetric hyperbolic
%B I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.
%R 1998LRR.....1...11J
%A Jones, Aled; Lasenby, Anthony N.
%F AA(Global Sustainability Institute (GSI) at Anglia Ruskin University) AB(Mullard Radio Astronomy Observatory, Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, U.K.)
%J Living Reviews in Relativity, vol. 1, no. 11
%D 09/1998
%T The Cosmic Microwave Background
%C (c) The author(s)
%G Physical Cosmology
%U http://www.livingreviews.org/lrr-1998-11
%I HTML: http://www.livingreviews.org/lrr-1998-11; PDF: http://relativity.livingreviews.org/Articles/lrr-1998-11/download/lrr-1998-11Color.pdf; DOI: 10.1007/lrr-1998-11
%B We present a brief review of current theory and observations of the cosmic microwave background (CMB). New predictions for cosmological defect theories and an overview of the inflationary theory are discussed. Recent results from various observations of the anisotropies of the microwave background are described and a summary of the proposed experiments is presented. A new analysis technique based on Bayesian statistics that can be used to reconstruct the underlying sky fluctuations is summarised. Current CMB data is used to set some preliminary constraints on the values of fundamental cosmological parameters $\Omega$ and $H_\circ$ using the maximum likelihood technique. In addition, secondary anisotropies due to the Sunyaev-Zel'dovich effect are described.
%R 1998LRR.....1...12W
%A Wambsganss, Joachim
%F AA(Astronomisches Rechen-Institut (ARI), Mönchhofstr. 12-14, D-69120 Heidelberg, Germany)
%J Living Reviews in Relativity, vol. 1, no. 12
%D 11/1998
%T Gravitational Lensing in Astronomy
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-1998-12
%I HTML: http://www.livingreviews.org/lrr-1998-12; PDF: http://relativity.livingreviews.org/Articles/lrr-1998-12/download/lrr-1998-12Color.pdf; DOI: 10.1007/lrr-1998-12
%B Deflection of light by gravity was predicted by General Relativity and observationally confirmed in 1919. In the following decades, various aspects of the gravitational lens effect were explored theoretically. Among them were: the possibility of multiple or ring-like images of background sources, the use of lensing as a gravitational telescope on very faint and distant objects, and the possibility of determining Hubble's constant with lensing. It is only relatively recently, (after the discovery of the first doubly imaged quasar in 1979), that gravitational lensing has became an observational science. Today lensing is a booming part of astrophysics.
In addition to multiply-imaged quasars, a number of other aspects of lensing have been discovered: For example, giant luminous arcs, quasar microlensing, Einstein rings, galactic microlensing events, arclets, and weak gravitational lensing. At present, literally hundreds of individual gravitational lens phenomena are known.
Although still in its childhood, lensing has established itself as a very useful astrophysical tool with some remarkable successes. It has contributed significant new results in areas as different as the cosmological distance scale, the large scale matter distribution in the universe, mass and mass distribution of galaxy clusters, the physics of quasars, dark matter in galaxy halos, and galaxy structure. Looking at these successes in the recent past we predict an even more luminous future for gravitational lensing.
%R 1998LRR.....1...13L
%A Loll, Renate
%F AA(Institute for Mathematics, Astrophysics and Particle Physics, Faculty of Science, Radboud University Nijmegen)
%J Living Reviews in Relativity, vol. 1, no. 13
%D 12/1998
%T Discrete Approaches to Quantum Gravity in Four Dimensions
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-1998-13
%I HTML: http://www.livingreviews.org/lrr-1998-13; PDF: http://relativity.livingreviews.org/Articles/lrr-1998-13/download/lrr-1998-13Color.pdf; DOI: 10.1007/lrr-1998-13
%B The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation; quantum Regge calculus; and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.
%R 1999LRR.....2....1M
%A Müller, Ingo
%F AA(Technical University Berlin, Thermodynamik, D-10623 Berlin, Germany)
%J Living Reviews in Relativity, vol. 2, no. 1
%D 06/1999
%T Speeds of Propagation in Classical and Relativistic Extended Thermodynamics
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-1999-1
%I HTML: http://www.livingreviews.org/lrr-1999-1; PDF: http://relativity.livingreviews.org/Articles/lrr-1999-1/download/lrr-1999-1Color.pdf; DOI: 10.1007/lrr-1999-1
%K Thermodynamics
%B The Navier-Stokes-Fourier theory of viscous, heat-conducting fluids provides parabolic equations and thus predicts infinite pulse speeds. Naturally this feature has disqualified the theory for relativistic thermodynamics which must insist on finite speeds and, moreover, on speeds smaller than $c$. The attempts at a remedy have proved heuristically important for a new systematic type of thermodynamics: Extended thermodynamics. That new theory has symmetric hyperbolic field equations and thus it provides finite pulse speeds. Extended thermodynamics is a whole hierarchy of theories with an increasing number of fields when gradients and rates of thermodynamic processes become steeper and faster. The first stage in this hierarchy is the 14-field theory which may already be a useful tool for the relativist in many applications. The 14 fields -- and further fields -- are conveniently chosen from the moments of the kinetic theory of gases. The hierarchy is complete only when the number of fields tends to infinity. In that case the pulse speed of non-relativistic extended thermodynamics tends to infinity while the pulse speed of relativistic extended thermodynamics tends to $c$, the speed of light. In extended thermodynamics symmetric hyperbolicity -- and finite speeds -- are implied by the concavity of the entropy density. This is still true in relativistic thermodynamics for a privileged entropy density which is the entropy density of the rest frame for non-degenerate gases.
%R 1999LRR.....2....2K
%A Kokkotas, Kostas D.; Schmidt, Bernd G.
%F AA(Institute for Astronomy and Astrophysics (IAAT) of the Eberhard-Karls-University Tübingen, D-72076 Tübingen, Auf der Morgenstelle 10, Germany) AB(Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Golm, Germany)
%J Living Reviews in Relativity, vol. 2, no. 2
%D 09/1999
%T Quasi-Normal Modes of Stars and Black Holes
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-1999-2
%I HTML: http://www.livingreviews.org/lrr-1999-2; PDF: http://relativity.livingreviews.org/Articles/lrr-1999-2/download/lrr-1999-2Color.pdf; DOI: 10.1007/lrr-1999-2
%B Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.
%R 2000LRR.....3....5C
%A Cook, Gregory B.
%F AA(Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109-7507, U.S.A.)
%J Living Reviews in Relativity, vol. 3, no. 5
%D 11/2000
%T Initial Data for Numerical Relativity
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2000-5
%I HTML: http://www.livingreviews.org/lrr-2000-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2000-5/download/lrr-2000-5Color.pdf; DOI: 10.1007/lrr-2000-5
%K ADM formalism, Binary systems, Black holes, Neutron stars, Initial value problem, Constraint equations, Numerical relativity
%B Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy initial data in the 3+1 decomposition of Einstein's equations. We will then explore how these formalisms have been used in constructing initial data for spacetimes containing black holes and neutron stars. In the topics discussed, emphasis is placed on those issues that are important for obtaining astrophysically realistic initial data for compact binary coalescence.
%R 2001LRR.....4....1C
%A Carroll, Sean M.
%F AA(Department of Physics, California Institute of Technology, MC 452-48, 1200 East California Boulevard, Pasadena, CA 91125, U.S.A.)
%J Living Reviews in Relativity, vol. 4, no. 1
%D 02/2001
%T The Cosmological Constant
%C (c) The author(s)
%G Physical Cosmology
%U http://www.livingreviews.org/lrr-2001-1
%I HTML: http://www.livingreviews.org/lrr-2001-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2001-1/download/lrr-2001-1Color.pdf; DOI: 10.1007/lrr-2001-1
%K cosmology, vacuum energy, cosmological constant
%B This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.
%R 2001LRR.....4....2A
%A Anninos, Peter
%F AA(University of California, Lawrence Livermore National Laboratory)
%J Living Reviews in Relativity, vol. 4, no. 2
%D 03/2001
%T Computational Cosmology: From the Early Universe to the Large Scale Structure
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2001-2
%I HTML: http://www.livingreviews.org/lrr-2001-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2001-2/download/lrr-2001-2Color.pdf; DOI: 10.1007/lrr-2001-2
%K physical cosmology, numerical methods, relativistic cosmology
%B In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations (and numerical methods) applied to specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark-hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.
%R 2001LRR.....4....6W
%A Wald, Robert M.
%F AA(Enrico Fermi Institute and Department of Physics, University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637-1433, U.S.A.)
%J Living Reviews in Relativity, vol. 4, no. 6
%D 07/2001
%T The Thermodynamics of Black Holes
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2001-6
%I HTML: http://www.livingreviews.org/lrr-2001-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2001-6/download/lrr-2001-6Color.pdf; DOI: 10.1007/lrr-2001-6
%K entropy bounds, thermodynamics, quantum field theory, black hole thermodynamics, variational methods, black holes, generalized second law, Euclidean methods, statistical mechanics, quantum gravity, event horizons, Killing horizons, Hawking radiation
%B We review the present status of black hole thermodynamics. Our review includes discussion of classical black hole thermodynamics, Hawking radiation from black holes, the generalized second law, and the issue of entropy bounds. A brief survey also is given of approaches to the calculation of black hole entropy. We conclude with a discussion of some unresolved open issues.
%R 2002LRR.....5....1B
%A Berger, Beverly K.
%F AA(Physics Department, Oakland University, Rochester, MI 48309, U.S.A. and Physics Division, National Science Foundation, 4201 Wilson Blvd., Arlington, VA 22230 U.S.A.)
%J Living Reviews in Relativity, vol. 5, no. 1
%D 01/2002
%T Numerical Approaches to Spacetime Singularities
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2002-1
%I HTML: http://www.livingreviews.org/lrr-2002-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2002-1/download/lrr-2002-1Color.pdf; DOI: 10.1007/lrr-2002-1
%K singularities, numerical relativity
%B This Living Review updates a previous version which is itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.
%R 2002LRR.....5....4S
%A Sumner, Timothy J.
%F AA(Astrophysics Group, Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BZ, U.K.)
%J Living Reviews in Relativity, vol. 5, no. 4
%D 07/2002
%T Experimental Searches for Dark Matter
%C (c) The author(s)
%G Physical Cosmology
%U http://www.livingreviews.org/lrr-2002-4
%I HTML: http://www.livingreviews.org/lrr-2002-4; PDF: http://relativity.livingreviews.org/Articles/lrr-2002-4/download/lrr-2002-4Color.pdf; DOI: 10.1007/lrr-2002-4
%K experimental dark matter search
%B There is now an enormously rich variety of experimental techniques being brought to bear on experimental searches for dark matter, covering a wide range of suggested forms for it. The existence of "dark matter", in some form or other, is inferred from a number of relatively simple observations and the problem has been known for over half a century. To explain "dark matter" is one of the foremost challenges today -- the answer will be of fundamental importance to cosmologists, astrophysicists, particle physicists, and general relativists. In this article, I will give a brief review of the observational evidence (concentrating on areas of current significant activity), followed by an equally brief summary of candidate solutions for the 'dark matter'. I will then discuss experimental searches, both direct and indirect. Finally, I will offer prospects for the future.
%R 2002LRR.....5....5B
%A Bern, Zvi
%F AA(Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, CA 90095, U.S.A.)
%J Living Reviews in Relativity, vol. 5, no. 5
%D 07/2002
%T Perturbative Quantum Gravity and its Relation to Gauge Theory
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2002-5
%I HTML: http://www.livingreviews.org/lrr-2002-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2002-5/download/lrr-2002-5Color.pdf; DOI: 10.1007/lrr-2002-5
%K supergravity, quantum gravity, gauge theory
%B In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on $D$-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input thegravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.
%R 2003LRR.....6....1A
%A Ashby, Neil
%F AA(Dept. of Physics, University of Colorado, Boulder, CO 80309-0390, U.S.A.)
%J Living Reviews in Relativity, vol. 6, no. 1
%D 01/2003
%T Relativity in the Global Positioning System
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2003-1
%I HTML: http://www.livingreviews.org/lrr-2003-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2003-1/download/lrr-2003-1Color.pdf; DOI: 10.1007/lrr-2003-1
%B The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work. This paper discusses the conceptual basis, founded on special and general relativity, for navigation using GPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalence principle, the Sagnac effect, time dilation, gravitational frequency shifts, and relativity of synchronization. Experimental tests of relativity obtained with a GPS receiver aboard the TOPEX/POSEIDON satellite will be discussed. Recently frequency jumps arising from satellite orbit adjustments have been identified as relativistic effects. These will be explained and some interesting applications of GPS will be discussed.
%R 2003LRR.....6....3S
%A Stergioulas, Nikolaos
%F AA(Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, 54124
Greece)
%J Living Reviews in Relativity, vol. 6, no. 3
%D 06/2003
%T Rotating Stars in Relativity
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-2003-3
%I HTML: http://www.livingreviews.org/lrr-2003-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2003-3/download/lrr-2003-3Color.pdf; DOI: 10.1007/lrr-2003-3
%K rotation, oscillations, numerical relativity, relativistic stars, stability
%B Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.
%R 2003LRR.....6....5S
%A Stairs, Ingrid H.
%F AA(Dept. of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada)
%J Living Reviews in Relativity, vol. 6, no. 5
%D 09/2003
%T Testing General Relativity with Pulsar Timing
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2003-5
%I HTML: http://www.livingreviews.org/lrr-2003-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2003-5/download/lrr-2003-5Color.pdf; DOI: 10.1007/lrr-2003-5
%K pulsars, astronomical observations, theories of gravity, neutron stars, gravitational radiation, binary systems, white dwarfs, tests of relativistic gravity
%B Pulsars of very different types, including isolated objects and binaries (with short- and long-period orbits, and white-dwarf and neutron-star companions) provide the means to test both the predictions of general relativity and the viability of alternate theories of gravity. This article presents an overview of pulsars, then discusses the current status of and future prospects for tests of equivalence-principle violations and strong-field gravitational experiments.
%R 2003LRR.....6....6S
%A Sasaki, Misao; Tagoshi, Hideyuki
%F AA(Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan) AB(Department of Earth and Space Science, Osaka University, Toyonaka, Osaka 560-0043, Japan)
%J Living Reviews in Relativity, vol. 6, no. 6
%D 11/2003
%T Analytic Black Hole Perturbation Approach to Gravitational Radiation
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2003-6
%I HTML: http://www.livingreviews.org/lrr-2003-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2003-6/download/lrr-2003-6Color.pdf; DOI: 10.1007/lrr-2003-6
%K Post-Newtonian expansion, Teukolsky equation
%B We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge–Wheeler type equation that reduces to the standard Klein–Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently), the Teukolsky equation is used directly in its original form. The former’s advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes to higher and higher post-Newtonian orders. In contrast, the latter’s advantage is that a systematic calculation to higher post-Newtonian orders can be implemented relatively easily, but otherwise, it is so mathematical that it is hard to understand the interplay of higher order terms. In this paper, we review both methods so that their pros and cons may be seen clearly. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.
%R 2003LRR.....6....7M
%A Martí, José Maria; Müller, Ewald
%F AA(Departamento de Astronomía y Astrofísica, Universidad de Valencia, 46100 Burjassot (Valencia), Spain) AB(Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching, Germany)
%J Living Reviews in Relativity, vol. 6, no. 7
%D 12/2003
%T Numerical Hydrodynamics in Special Relativity
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2003-7
%I HTML: http://www.livingreviews.org/lrr-2003-7; PDF: http://relativity.livingreviews.org/Articles/lrr-2003-7/download/lrr-2003-7Color.pdf; DOI: 10.1007/lrr-2003-7
%B This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
%R 2004LRR.....7....1F
%A Frauendiener, Jörg
%F AA(Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9010, New Zealand)
%J Living Reviews in Relativity, vol. 7, no. 1
%D 02/2004
%T Conformal Infinity
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2004-1
%I HTML: http://www.livingreviews.org/lrr-2004-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2004-1/download/lrr-2004-1Color.pdf; DOI: 10.1007/lrr-2004-1
%B The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.
%R 2004LRR.....7....2G
%A Goenner, Hubert F. M.
%F AA(University of Göttingen, Institut für Theoretische Physik, Tammannstr. 1, D-37077 Göttingen, Germany)
%J Living Reviews in Relativity, vol. 7, no. 2
%D 02/2004
%T On the History of Unified Field Theories
%C (c) The author(s)
%G History of Relativity
%U http://www.livingreviews.org/lrr-2004-2
%I HTML: http://www.livingreviews.org/lrr-2004-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2004-2/download/lrr-2004-2Color.pdf; DOI: 10.1007/lrr-2004-2
%K history of science, unified field theories
%B This article is intended to give a review of the history of the classical aspects of unified field theories in the 20th century. It includes brief technical descriptions of the theories suggested, short biographical notes concerning the scientists involved, and an extensive bibliography. The present first installment covers the time span between 1914 and 1933, i.e., when Einstein was living and working in Berlin - with occasional digressions into other periods. Thus, the main theme is the unification of the electromagnetic and gravitational fields augmented by short-lived attempts to include the matter field described by Schrödinger's or Dirac's equations. While my focus lies on the conceptual development of the field, by also paying attention to the interaction of various schools of mathematicians with the research done by physicists, some prosopographical remarks are included.
%R 2004LRR.....7....5B
%A Burgess, Cliff P.
%F AA(Department of Physics and Astronomy, ABB-324, McMaster University, 1280 Main St. W, Hamilton, ON, L8S 4M1, Canada)
%J Living Reviews in Relativity, vol. 7, no. 5
%D 04/2004
%T Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2004-5
%I HTML: http://www.livingreviews.org/lrr-2004-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2004-5/download/lrr-2004-5Color.pdf; DOI: 10.1007/lrr-2004-5
%K effective field theories, quantum gravity, general theory of relativity
%B This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems, ideas which provide the theoretical foundations for the modern use of general relativity as a theory from which precise predictions are possible.
%R 2004LRR.....7....8L
%A Lahav, Ofer; Suto, Yasushi
%F AA(Department of Physics and Astronomy, University of London, Gower Street, London WC1E 6BT, U.K. and Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, U.K.) AB(Department of Physics and Research Center for the Early Universe, The University of Tokyo, Tokyo 113-0033, Japan)
%J Living Reviews in Relativity, vol. 7, no. 8
%D 07/2004
%T Measuring our Universe from Galaxy Redshift Surveys
%C (c) The author(s)
%G Physical Cosmology
%U http://www.livingreviews.org/lrr-2004-8
%I HTML: http://www.livingreviews.org/lrr-2004-8; PDF: http://relativity.livingreviews.org/Articles/lrr-2004-8/download/lrr-2004-8Color.pdf; DOI: 10.1007/lrr-2004-8
%K large-scale structure of universe, cosmology, statistical methods, dark matter
%B Galaxy redshift surveys have achieved significant progress over the last couple of decades. Those surveys tell us in the most straightforward way what our local Universe looks like. While the galaxy distribution traces the bright side of the Universe, detailed quantitative analyses of the data have even revealed the dark side of the Universe dominated by non-baryonic dark matter as well as more mysterious dark energy (or Einstein's cosmological constant). We describe several methodologies of using galaxy redshift surveys as cosmological probes, and then summarize the recent results from the existing surveys. Finally we present our views on the future of redshift surveys in the era of precision cosmology.
%R 2004LRR.....7....9P
%A Perlick, Volker
%F AA(Physics Department, Lancaster University, Lancaster, LA1 4YB, U.K.)
%J Living Reviews in Relativity, vol. 7, no. 9
%D 09/2004
%T Gravitational Lensing from a Spacetime Perspective
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2004-9
%I HTML: http://www.livingreviews.org/lrr-2004-9; PDF: http://relativity.livingreviews.org/Articles/lrr-2004-9/download/lrr-2004-9Color.pdf; DOI: 10.1007/lrr-2004-9
%K gravitational lenses, differential geometry
%B The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.
%R 2004LRR.....7...10A
%A Ashtekar, Abhay; Krishnan, Badri
%F AA(Institute for Gravitational Physics and Geometry, Pennsylvania State University, University Park, PA 16801, U.S.A. and Kavli Institute of Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, U.S.A. and Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm, Germany and Erwin-Schrödinger-Institut, Boltzmanngasse 9, 1090 Vienna, Austria) AB(Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm, Germany and Erwin-Schrödinger-Institut, Boltzmanngasse 9, 1090 Vienna, Austria)
%J Living Reviews in Relativity, vol. 7, no. 10
%D 12/2004
%T Isolated and Dynamical Horizons and Their Applications
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2004-10
%I HTML: http://www.livingreviews.org/lrr-2004-10; PDF: http://relativity.livingreviews.org/Articles/lrr-2004-10/download/lrr-2004-10Color.pdf; DOI: 10.1007/lrr-2004-10
%K quantum gravity, generalized thermodynamics, black holes
%B Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modelled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity, and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity, suggested a phenomenological model for hairy black holes, provided novel techniques to extract physics from numerical simulations, and led to new laws governing the dynamics of black holes in exact general relativity.
%R 2005LRR.....8....1C
%A Carlip, Steven
%F AA(Department of Physics, University of California, Davis, CA 95616, U.S.A.)
%J Living Reviews in Relativity, vol. 8, no. 1
%D 01/2005
%T Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2005-1
%I HTML: http://www.livingreviews.org/lrr-2005-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2005-1/download/lrr-2005-1Color.pdf; DOI: 10.1007/lrr-2005-1
%K quantum cosmology, quantum gravity, 2+1 gravity
%B In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.
%R 2005LRR.....8....5M
%A Mattingly, David
%F AA(Department of Physics, University of California at Davis, Davis, CA 95616, U.S.A.)
%J Living Reviews in Relativity, vol. 8, no. 5
%D 09/2005
%T Modern Tests of Lorentz Invariance
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2005-5
%I HTML: http://www.livingreviews.org/lrr-2005-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2005-5/download/lrr-2005-5Color.pdf; DOI: 10.1007/lrr-2005-5
%K Lorentz invariance, Quantum gravity phenomenology
%B Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.
%R 2005LRR.....8....6R
%A Rendall, Alan D.
%F AA(Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, D-14424 Golm, Germany)
%J Living Reviews in Relativity, vol. 8, no. 6
%D 10/2005
%T Theorems on Existence and Global Dynamics for the Einstein Equations
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2005-6
%I HTML: http://www.livingreviews.org/lrr-2005-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2005-6/download/lrr-2005-6Color.pdf; DOI: 10.1007/lrr-2005-6
%B This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.
%R 2005LRR.....8....8M
%A Merritt, David; Milosavljević, Miloš
%F AA(Center for Computational Relativity and Gravitation (CCRG), Rochester Institute of Technology, Rochester, NY, U.S.A.) AB(The University of Texas, C1400, Department of Astronomy, 2511 Speedway, RLM 15.306, Austin, TX 78712, U.S.A.)
%J Living Reviews in Relativity, vol. 8, no. 8
%D 11/2005
%T Massive Black Hole Binary Evolution
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-2005-8
%I HTML: http://www.livingreviews.org/lrr-2005-8; PDF: http://relativity.livingreviews.org/Articles/lrr-2005-8/download/lrr-2005-8Color.pdf; DOI: 10.1007/lrr-2005-8
%B Coalescence of binary supermassive black holes (SBHs) would constitute the strongest sources of gravitational waves to be observed by LISA. While the formation of binary SBHs during galaxy mergers is almost inevitable, coalescence requires that the separation between binary components first drop by a few orders of magnitude, due presumably to interaction of the binary with stars and gas in a galactic nucleus. This article reviews the observational evidence for binary SBHs and discusses how they would evolve. No completely convincing case of a bound, binary SBH has yet been found, although a handful of systems (e.g. interacting galaxies; remnants of galaxy mergers) are now believed to contain two SBHs at projected separations of <~ 1kpc. N-body studies of binary evolution in gas-free galaxies have reached large enough particle numbers to reproduce the slow, “diffusive” refilling of the binary’s loss cone that is believed to characterize binary evolution in real galactic nuclei. While some of the results of these simulations - e.g. the binary hardening rate and eccentricity evolution - are strongly N-dependent, others - e.g. the “damage” inflicted by the binary on the nucleus - are not. Luminous early-type galaxies often exhibit depleted cores with masses of ~ 1-2 times the mass of their nuclear SBHs, consistent with the predictions of the binary model. Studies of the interaction of massive binaries with gas are still in their infancy, although much progress is expected in the near future. Binary coalescence has a large influence on the spins of SBHs, even for mass ratios as extreme as 10:1, and evidence of spin-flips may have been observed.
%R 2005LRR.....8....9P
%A Plefka, Jan
%F AA(Humboldt Universität zu Berlin, Institut für Physik, Newtonstrasse 15, D-12489 Berlin, Germany)
%J Living Reviews in Relativity, vol. 8, no. 9
%D 11/2005
%T Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence
%C (c) The author(s)
%G String Theory and Gravitation
%U http://www.livingreviews.org/lrr-2005-9
%I HTML: http://www.livingreviews.org/lrr-2005-9; PDF: http://relativity.livingreviews.org/Articles/lrr-2005-9/download/lrr-2005-9Color.pdf; DOI: 10.1007/lrr-2005-9
%K String Theory, Supersymmetric Yang-Mills, AdS/CFT Correspondence
%B In this introductory review we discuss dynamical tests of the AdS_5 × S^5 string/N = 4 Super Yang-Mills duality. After a brief introduction to AdS/CFT, we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S^5. The energies of the folded and circular spinning string solutions rotating on a S^3 within the S^5 are derived, which yield all-loop predictions for the dual gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator of N = 4 Super Yang-Mills in a minimal SU(2) subsector, and we display its reformulation in terms of a Heisenberg s = 1/2 spin chain along with the coordinate Bethe ansatz for its explicit diagonalization. In order to make contact to the spinning string energies, we then study the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the matching with the folded and closed string result at this loop order. Finally, the known gauge theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe equations. This uncovers discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies, and the implications of this are discussed. Along the way, we comment on further developments and generalizations of the subject and point to the relevant literature.
%R 2006LRR.....9....1A
%A Armstrong, John W.
%F AA(Jet Propulsion Laboratory, California Institute of Technology, Mail Stop 238-725, 4800 Oak Grove Dr., Pasadena, CA 91109-8001, U.S.A.)
%J Living Reviews in Relativity, vol. 9, no. 1
%D 01/2006
%T Low-Frequency Gravitational Wave Searches Using Spacecraft Doppler Tracking
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2006-1
%I HTML: http://www.livingreviews.org/lrr-2006-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2006-1/download/lrr-2006-1Color.pdf; DOI: 10.1007/lrr-2006-1
%K Cassini, Doppler stability, Doppler tracking, frequency stability, gravitational wave detectors, radio
%B This paper discusses spacecraft Doppler tracking, the current-generation detector technology used in the low-frequency (~millihertz) gravitational wave band. In the Doppler method the earth and a distant spacecraft act as free test masses with a ground-based precision Doppler tracking system continuously monitoring the earth-spacecraft relative dimensionless velocity $2 \Delta v/c = \Delta \nu/\nu_0$, where $\Delta \nu$ is the Doppler shift and $\nu_0$ is the radio link carrier frequency. A gravitational wave having strain amplitude $h$ incident on the earth-spacecraft system causes perturbations of order $h$ in the time series of $\Delta \nu/\nu_0$. Unlike other detectors, the ~1-10 AU earth-spacecraft separation makes the detector large compared with millihertz-band gravitational wavelengths, and thus times-of-flight of signals and radio waves through the apparatus are important. A burst signal, for example, is time-resolved into a characteristic signature: three discrete events in the Doppler time series. I discuss here the principles of operation of this detector (emphasizing transfer functions of gravitational wave signals and the principal noises to the Doppler time series), some data analysis techniques, experiments to date, and illustrations of sensitivity and current detector performance. I conclude with a discussion of how gravitational wave sensitivity can be improved in the low-frequency band.
%R 2006LRR.....9....5N
%A Niedermaier, Max; Reuter, Martin
%F AA(Laboratoire de Mathematiques et Physique Theorique, CNRS/UMR 6083, Université de Tours, Parc de Grandmont, 37200 Tours, France) AB(Institute of Physics, University of Mainz, Staudingerweg 7, 55099 Mainz, Germany)
%J Living Reviews in Relativity, vol. 9, no. 5
%D 12/2006
%T The Asymptotic Safety Scenario in Quantum Gravity
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2006-5
%I HTML: http://www.livingreviews.org/lrr-2006-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2006-5/download/lrr-2006-5Color.pdf; DOI: 10.1007/lrr-2006-5
%K quantum gravity
%B The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
%R 2007LRR....10....1A
%A Andersson, Nils; Comer, Gregory L.
%F AA(School of Mathematics, University of Southampton, Southampton SO17 1BJ, U.K.) AB(Department of Physics & Center for Fluids at All Scales, Saint Louis University, St. Louis, MO, 63156-0907, U.S.A.)
%J Living Reviews in Relativity, vol. 10, no. 1
%D 01/2007
%T Relativistic Fluid Dynamics: Physics for Many Different Scales
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-2007-1
%I HTML: http://www.livingreviews.org/lrr-2007-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2007-1/download/lrr-2007-1Color.pdf; DOI: 10.1007/lrr-2007-1
%K fluid dynamics, relativistic hydrodynamics, relativistic astrophysics, variational methods, classical field theory
%B The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process, an understanding of bulk features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model systems as ``small'' as heavy ions in collisions, and as large as the Universe itself, with ``intermediate'' sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theoretical physics underpinnings of the relativistic (multiple) fluid model. We focus on the variational principle approach championed by Brandon Carter and his collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the ``standard'' text-book derivation of the equations of motion from the divergence of the stress-energy tensor in that one explicitly obtains the relativistic Euler equation as an ``integrability'' condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications of the general theory.
%R 2007LRR....10....2F
%A Futamase, Toshifumi; Itoh, Yousuke
%F AA(Astronomical Institute, Tohoku University, Sendai 980-8578, Japan) AB(Astronomical Institute, Tohoku University, Sendai 980-8578, Japan)
%J Living Reviews in Relativity, vol. 10, no. 2
%D 03/2007
%T The Post-Newtonian Approximation for Relativistic Compact Binaries
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2007-2
%I HTML: http://www.livingreviews.org/lrr-2007-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2007-2/download/lrr-2007-2Color.pdf; DOI: 10.1007/lrr-2007-2
%K post-Newtonian approximations, post-Newtonian expansion, equations of motion, relativistic binary systems, binary dynamics
%B We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.
%R 2007LRR....10....3T
%A Thornburg, Jonathan
%F AA(Department of Astronomy, Indiana University, Swain West 312, 727 East Third Street, Bloomington, IN 47405, U.S.A.)
%J Living Reviews in Relativity, vol. 10, no. 3
%D 06/2007
%T Event and Apparent Horizon Finders for 3+1 Numerical Relativity
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2007-3
%I HTML: http://www.livingreviews.org/lrr-2007-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2007-3/download/lrr-2007-3Color.pdf; DOI: 10.1007/lrr-2007-3
%K numerical relativity, ADM formalism, black holes, null surfaces, trapped surfaces, partial differential equations, apparent horizons, event horizons, numerical algorithms
%B Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3+1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time: it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed.
There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate.
In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Theta. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most “apparent horizon” finders actually find MOTSs.
There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well and are fairly easy to program. In slices with no continuous symmetries, spectral integral-iteration algorithms and elliptic-PDE algorithms are fast and accurate, but require good initial guesses to converge. In many cases, Schnetter’s “pretracking” algorithm can greatly improve an elliptic-PDE algorithm’s robustness. Flow algorithms are generally quite slow but can be very robust in their convergence. Minimization methods are slow and relatively inaccurate in the context of a finite differencing simulation, but in a spectral code they can be relatively faster and more robust.
%R 2007LRR....10....5G
%A Gundlach, Carsten; Martín-García, José M.
%F AA(Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, U.K.) AB(Wolfram Research, Inc., 100 Trade Center Drive, Champaign, Illinois 61820, USA)
%J Living Reviews in Relativity, vol. 10, no. 5
%D 12/2007
%T Critical Phenomena in Gravitational Collapse
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2007-5
%I HTML: http://www.livingreviews.org/lrr-2007-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2007-5/download/lrr-2007-5Color.pdf; DOI: 10.1007/lrr-2007-5
%K Numerical relativity, Black holes, Naked singularities, Self-similarity, Critical phenomena, Scaling laws, Stability, Gravitational collapse, Phase space
%B As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity. Universality, power-law scaling of the black hole mass, and scale echoing have given rise to the term “critical phenomena”. They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar. Critical phenomena give a natural route from smooth initial data to arbitrarily large curvatures visible from infinity, and are therefore likely to be relevant for cosmic censorship, quantum gravity, astrophysics, and our general understanding of the dynamics of general relativity.
%R 2008LRR....11....1H
%A Henneaux, Marc; Persson, Daniel; Spindel, Philippe
%F AA(Physique Théorique et Mathématique, Université Libre de Bruxelles & International Solvay Institutes, Boulevard du Triomphe, ULB – C.P. 231, B-1050 Bruxelles, Belgium) AB(Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland) AC(Service de Mécanique et Gravitation, Université de Mons-Hainaut, Académie Wallonie-Bruxelles, Avenue du Champ de Mars 6, B-7000 Mons, Belgium)
%J Living Reviews in Relativity, vol. 11, no. 1
%D 04/2008
%T Spacelike Singularities and Hidden Symmetries of Gravity
%C (c) The author(s)
%G String Theory and Gravitation
%U http://www.livingreviews.org/lrr-2008-1
%I HTML: http://www.livingreviews.org/lrr-2008-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-1/download/lrr-2008-1Color.pdf; DOI: 10.1007/lrr-2008-1
%K hidden symmetries, duality, Kac-Moody algebras
%B We review the intimate connection between (super-)gravity close to a spacelike singularity (the “BKL-limit”) and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E_10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.
%R 2008LRR....11....2C
%A Cirkel-Bartelt, Vanessa
%F AA(Technische Universität Dortmund, Department of Human Sciences and Theology (14), Emil-Figge-Str. 50, 44221 Dortmund, Germany and Interdisciplinary Center for Science and Technology Studies: Normative and Historical Perspectives (IZWT), Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal)
%J Living Reviews in Relativity, vol. 11, no. 2
%D 05/2008
%T History of Astroparticle Physics and its Components
%C (c) The author(s)
%G History of Relativity
%U http://www.livingreviews.org/lrr-2008-2
%I HTML: http://www.livingreviews.org/lrr-2008-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-2/download/lrr-2008-2Color.pdf; DOI: 10.1007/lrr-2008-2
%K astroparticle physics, history of physics, philosophy of physics
%B This article gives an outline of the historical events that led to the formation of contemporary astroparticle physics. As a starting point for analyzing the history of astroparticle physics this article will review the various, yet scattered pieces of historical work that have been done so far. To make the picture more complete it will then give a brief survey of the most important fields that have played a role in the development of astroparticle physics as we know it today. It will conclude with an overview of the historical questions that are still open and the rich philosophical implications that lie behind those questions.
%R 2008LRR....11....3H
%A Hu, Bei Lok; Verdaguer, Enric
%F AA(Department of Physics, University of Maryland, College Park, Maryland 20742-4111, U.S.A.) AB(Departament de Física Fonamental and C.E.R. in Astrophysics, Particles and Cosmology
Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona, Spain)
%J Living Reviews in Relativity, vol. 11, no. 3
%D 05/2008
%T Stochastic Gravity: Theory and Applications
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2008-3
%I HTML: http://www.livingreviews.org/lrr-2008-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-3/download/lrr-2008-3Color.pdf; DOI: 10.1007/lrr-2008-3
%K stochastic gravity, semiclassical gravity, quantum gravity, quantum fields in curved space, inflation, structure formation, black holes
%B Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out directions for further developments and applications.
%R 2008LRR....11....4B
%A Bojowald, Martin
%F AA(Institute for Gravitational Physics and Geometry, The Pennsylvania State University, University Park, PA 16802, U.S.A.)
%J Living Reviews in Relativity, vol. 11, no. 4
%D 07/2008
%T Loop Quantum Cosmology
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2008-4
%I HTML: http://www.livingreviews.org/lrr-2008-4; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-4/download/lrr-2008-4Color.pdf; DOI: 10.1007/lrr-2008-4
%K Ashtekar variables, Big Bang, canonical quantum gravity, cosmology, effective equations, equations of motion, inflation, quantum cosmology, singularities, symmetry, time, difference equations
%B Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.
%R 2008LRR....11....5R
%A Rovelli, Carlo
%F AA(Centre de Physique Théorique de Luminy, Case 907, Luminy, F-13288 Marseille, France)
%J Living Reviews in Relativity, vol. 11, no. 5
%D 07/2008
%T Loop Quantum Gravity
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2008-5
%I HTML: http://www.livingreviews.org/lrr-2008-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-5/download/lrr-2008-5Color.pdf; DOI: 10.1007/lrr-2008-5
%K Quantum gravity, Loop quantum gravity
%B The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein–Hawking black-hole entropy. (v) Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
%R 2008LRR....11....6E
%A Emparan, Roberto; Reall, Harvey S.
%F AA(Institució Catalana de Recerca i Estudis Avançats (ICREA), and Departament de Física Fonamental, Universitat de Barcelona, Marti i Franquès 1, E-08028 Barcelona, Spain) AB(Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom)
%J Living Reviews in Relativity, vol. 11, no. 6
%D 09/2008
%T Black Holes in Higher Dimensions
%C (c) The author(s)
%G String Theory and Gravitation
%U http://www.livingreviews.org/lrr-2008-6
%I HTML: http://www.livingreviews.org/lrr-2008-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-6/download/lrr-2008-6Color.pdf; DOI: 10.1007/lrr-2008-6
%K black holes, string theory, supergravity
%B We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers–Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.
%R 2008LRR....11....7F
%A Font, José A.
%F AA(Departamento de Astronomía y Astrofísica, Edificio de Investigación "Jeroni Muñoz", Universidad de Valencia, Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain)
%J Living Reviews in Relativity, vol. 11, no. 7
%D 09/2008
%T Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2008-7
%I HTML: http://www.livingreviews.org/lrr-2008-7; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-7/download/lrr-2008-7Color.pdf; DOI: 10.1007/lrr-2008-7
%K Hydrodynamics, Relativistic hydrodynamics, Numerical relativity, Magnetohydrodynamics
%B This article presents a comprehensive overview of numerical hydrodynamics and magnetohydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works.
%R 2008LRR....11....8L
%A Lorimer, Duncan R.
%F AA(West Virginia University, Department of Physics, PO Box 6415, Morgantown, WV 26506, U.S.A.)
%J Living Reviews in Relativity, vol. 11, no. 8
%D 11/2008
%T Binary and Millisecond Pulsars
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-2008-8
%I HTML: http://www.livingreviews.org/lrr-2008-8; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-8/download/lrr-2008-8Color.pdf; DOI: 10.1007/lrr-2008-8
%K pulsars
%B We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the known pulsar population to over 1800. There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy, and a further 140 pulsars in 26 of the Galactic globular clusters. Recent highlights include the discovery of the young relativistic binary system PSR J1906+0746, a rejuvination in globular cluster pulsar research including growing numbers of pulsars with masses in excess of $1.5\,M_{\odot}$, a precise measurement of relativistic spin precession in the double pulsar system and a Galactic millisecond pulsar in an eccentric (e=0.44) orbit around an unevolved companion.
%R 2008LRR....11....9P
%A Psaltis, Dimitrios
%F AA(Physics and Astronomy Departments, University of Arizona, Tucson, AZ 85721, U.S.A.)
%J Living Reviews in Relativity, vol. 11, no. 9
%D 11/2008
%T Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2008-9
%I HTML: http://www.livingreviews.org/lrr-2008-9; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-9/download/lrr-2008-9Color.pdf; DOI: 10.1007/lrr-2008-9
%K Neutron stars, Black holes, Tests of relativistic gravity
%B Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of using observations of such compact objects to probe some of the most intriguing general relativistic predictions in the strong-field regime: the absence of stable circular orbits near a compact object and the presence of event horizons around black-hole singularities. I discuss the need for a theoretical framework, within which future experiments will provide detailed, quantitative tests of gravity theories. Finally, I summarize the constraints imposed by current observations of neutron stars on potential deviations from general relativity.
%R 2008LRR....11...10C
%A Chamel, Nicolas; Haensel, Paweł
%F AA(Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, CP226, Boulevard du Triomphe B-1050 Brussels, Belgium) AB(Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland)
%J Living Reviews in Relativity, vol. 11, no. 10
%D 12/2008
%T Physics of Neutron Star Crusts
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-2008-10
%I HTML: http://www.livingreviews.org/lrr-2008-10; PDF: http://relativity.livingreviews.org/Articles/lrr-2008-10/download/lrr-2008-10Color.pdf; DOI: 10.1007/lrr-2008-10
%K astrophysics, neutron stars, pulsars, magnetars, soft gamma repeaters, supernova, elasticity, neutron star cooling, low-mass X-ray binaries, oscillations, structure, transport properties, conductivity, viscosity, neutrino, equation of state, neutron star crust, superfluidity, entrainment, two-fluid model, accretion, X-ray astronomy, gravitational waves, pulsar glitches, accreting neutron stars, deep crustal heating
%B The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.
%R 2009LRR....12....1G
%A Grandclément, Philippe; Novak, Jérôme
%F AA(Laboratoire Univers et Théories, UMR 8102 du C.N.R.S., Observatoire de Paris, F-92195 Meudon Cedex, France) AB(Laboratoire Univers et Théories, UMR 8102 du C.N.R.S., Observatoire de Paris, F-92195 Meudon Cedex, France)
%J Living Reviews in Relativity, vol. 12, no. 1
%D 01/2009
%T Spectral Methods for Numerical Relativity
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2009-1
%I HTML: http://www.livingreviews.org/lrr-2009-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2009-1/download/lrr-2009-1Color.pdf; DOI: 10.1007/lrr-2009-1
%K Numerical relativity, Numerical methods
%B Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole–binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole–binary mergers.
%R 2009LRR....12....2S
%A Sathyaprakash, B.S.; Schutz, Bernard F.
%F AA(School of Physics and Astronomy, Cardiff University, Cardiff, U.K.) AB(School of Physics and Astronomy, Cardiff University, Cardiff, U.K. and Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam-Golm, Germany)
%J Living Reviews in Relativity, vol. 12, no. 2
%D 03/2009
%T Physics, Astrophysics and Cosmology with Gravitational Waves
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2009-2
%I HTML: http://www.livingreviews.org/lrr-2009-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2009-2/download/lrr-2009-2Color.pdf; DOI: 10.1007/lrr-2009-2
%K Gravitational wave sources, Data analysis, Gravitational waves, Gravitational wave detectors
%B Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.
%R 2009LRR....12....4S
%A Szabados, László B.
%F AA(Wigner Research Centre for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, P.O. Box 49, Hungary)
%J Living Reviews in Relativity, vol. 12, no. 4
%D 06/2009
%T Quasi-Local Energy-Momentum and Angular Momentum in General Relativity
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2009-4
%I HTML: http://www.livingreviews.org/lrr-2009-4; PDF: http://relativity.livingreviews.org/Articles/lrr-2009-4/download/lrr-2009-4Color.pdf; DOI: 10.1007/lrr-2009-4
%K Witten equations, Quasi-local mass, Quasi-local angular momentum, Quasi-local energy-momentum, General relativity
%B The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.
%R 2009LRR....12....5V
%A Vinet, Jean-Yves
%F AA(Observatoire de la Côte d’Azur (ARTEMIS), Université de Nice-Sophia Antipolis, 06304 Nice, France)
%J Living Reviews in Relativity, vol. 12, no. 5
%D 07/2009
%T On Special Optical Modes and Thermal Issues in Advanced Gravitational Wave Interferometric Detectors
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2009-5
%I HTML: http://www.livingreviews.org/lrr-2009-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2009-5/download/lrr-2009-5Color.pdf; DOI: 10.1007/lrr-2009-5
%K Gravitational radiation, Optics, Interferometry, Gravitational wave detectors
%B The sensitivity of present ground-based gravitational wave antennas is too low to detect many events per year. It has, therefore, been planned for years to build advanced detectors allowing actual astrophysical observations and investigations. In such advanced detectors, one major issue is to increase the laser power in order to reduce shot noise. However, this is useless if the thermal noise remains at the current level in the 100 Hz spectral region, where mirrors are the main contributors. Moreover, increasing the laser power gives rise to various spurious thermal effects in the same mirrors. The main goal of the present study is to discuss these issues versus the transverse structure of the readout beam, in order to allow comparison. A number of theoretical studies and experiments have been carried out, regarding thermal noise and thermal effects. We do not discuss experimental problems, but rather focus on some theoretical results in this context about arbitrary order Laguerre–Gauss beams, and other “exotic” beams.
%R 2010LRR....13....1F
%A Freise, Andreas; Strain, Kenneth A.
%F AA(School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK) AB(Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK)
%J Living Reviews in Relativity, vol. 13, no. 1
%D 02/2010
%T Interferometer Techniques for Gravitational-Wave Detection
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2010-1
%I HTML: http://www.livingreviews.org/lrr-2010-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2010-1/download/lrr-2010-1Color.pdf; DOI: 10.1007/lrr-2010-1
%K Gravitational wave detectors, Gravitational waves, Laser interferometry, Interferometer simulations, Finesse, Optics
%B Several km-scale gravitational-wave detectors have been constructed world wide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques, however, the complex optical layouts provide a new challenge. In this review we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.
%R 2010LRR....13....2R
%A Ringström, Hans
%F AA(Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden)
%J Living Reviews in Relativity, vol. 13, no. 2
%D 04/2010
%T Cosmic Censorship for Gowdy Spacetimes
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2010-2
%I HTML: http://www.livingreviews.org/lrr-2010-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2010-2/download/lrr-2010-2Color.pdf; DOI: 10.1007/lrr-2010-2
%K cosmic censorship, Cauchy problem, Gowdy models
%B Due to the complexity of Einstein’s equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.
%R 2010LRR....13....3D
%A De Felice, Antonio; Tsujikawa, Shinji
%F AA(Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kyoto, Japan) AB(Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan)
%J Living Reviews in Relativity, vol. 13, no. 3
%D 06/2010
%T f(R) Theories
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2010-3
%I HTML: http://www.livingreviews.org/lrr-2010-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2010-3/download/lrr-2010-3Color.pdf; DOI: 10.1007/lrr-2010-3
%K modified gravity, inflation, f(R) gravity, dark energy, cosmological perturbations
%B Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity – such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans–Dicke theory and Gauss–Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.
%R 2010LRR....13....4T
%A Turyshev, Slava G.; Toth, Viktor T.
%F AA(Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, U.S.A.) AB(Ottawa, ON K1N 9H5, Canada)
%J Living Reviews in Relativity, vol. 13, no. 4
%D 09/2010
%T The Pioneer Anomaly
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2010-4
%I HTML: http://www.livingreviews.org/lrr-2010-4; PDF: http://relativity.livingreviews.org/Articles/lrr-2010-4/download/lrr-2010-4Color.pdf; DOI: 10.1007/lrr-2010-4
%K Pioneer anomaly
%B Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20 – 70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ∼ 6 × 10–9 Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of aP = (8.74 ± 1.33) × 10–10 m/s2. This apparent violation of the Newton’s gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.
%R 2010LRR....13....5M
%A Maartens, Roy; Koyama, Kazuya
%F AA(Institute of Cosmology and Gravitation, Portsmouth University, Portsmouth PO12EG, U.K.) AB(Institute of Cosmology & Gravitation, University of Portsmouth, Portsmouth PO1 3FX, U.K.)
%J Living Reviews in Relativity, vol. 13, no. 5
%D 09/2010
%T Brane-World Gravity
%C (c) The author(s)
%G String Theory and Gravitation
%U http://www.livingreviews.org/lrr-2010-5
%I HTML: http://www.livingreviews.org/lrr-2010-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2010-5/download/lrr-2010-5Color.pdf; DOI: 10.1007/lrr-2010-5
%K Brane-world models, M theory
%B The observable universe could be a 1+3-surface (the “brane”) embedded in a 1+3+d-dimensional spacetime (the “bulk”), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the d extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak (∼ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity “leaks” into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall–Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at low energies – the 5-dimensional Dvali–Gabadadze–Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.
%R 2010LRR....13....6B
%A Barbero G., J. Fernando; Villaseñor, Eduardo J. S.
%F AA(Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain) AB(Instituto Gregorio Millán, Grupo de Modelización y Simulación Numérica, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain)
%J Living Reviews in Relativity, vol. 13, no. 6
%D 10/2010
%T Quantization of Midisuperspace Models
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2010-6
%I HTML: http://www.livingreviews.org/lrr-2010-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2010-6/download/lrr-2010-6Color.pdf; DOI: 10.1007/lrr-2010-6
%K Loop quantum gravity, Quantization, Quantum gravity, Midisuperspace
%B We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically-symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop-quantum-gravity-inspired methods.
%R 2010LRR....13....7M
%A Merkowitz, Stephen M.
%F AA(NASA Goddard Space Flight Center, Greenbelt, MD 20771, U.S.A.)
%J Living Reviews in Relativity, vol. 13, no. 7
%D 11/2010
%T Tests of Gravity Using Lunar Laser Ranging
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2010-7
%I HTML: http://www.livingreviews.org/lrr-2010-7; PDF: http://relativity.livingreviews.org/Articles/lrr-2010-7/download/lrr-2010-7Color.pdf; DOI: 10.1007/lrr-2010-7
%K General relativity, Tests of relativity
%B Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the past four decades. The three retroreflector arrays put on the Moon by the Apollo astronauts and the French built arrays on the Soviet Lunokhod rovers continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton’s gravitational constant. The relatively new ranging system at the Apache Point 3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly, it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retroreflectors are limiting the precision of the range measurements. In this article, we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.
%R 2011LRR....14....1F
%A Fryer, Chris L.; New, Kimberly C.B.
%F AA(Los Alamos National Laboratory, MS D409, CCS-2, Los Alamos, NM 87545, U.S.A.) AB(Los Alamos National Laboratory, MS T087, X-4 Los Alamos, New Mexico 87545, U.S.A.)
%J Living Reviews in Relativity, vol. 14, no. 1
%D 01/2011
%T Gravitational Waves from Gravitational Collapse
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2011-1
%I HTML: http://www.livingreviews.org/lrr-2011-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2011-1/download/lrr-2011-1Color.pdf; DOI: 10.1007/lrr-2011-1
%K Gravitational wave sources, Gravitational collapse
%B Gravitational-wave emission from stellar collapse has been studied for nearly four decades. Current state-of-the-art numerical investigations of collapse include those that use progenitors with more realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non-axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with ground-based and space-based interferometric observatories. This review covers the entire range of stellar collapse sources of gravitational waves: from the accretion-induced collapse of a white dwarf through the collapse down to neutron stars or black holes of massive stars to the collapse of supermassive stars.
%R 2011LRR....14....2U
%A Uzan, Jean-Philippe
%F AA(Institut d’Astrophysique de Paris, UMR-7095 du CNRS, Université Pierre et Marie Curie, 98 bis bd Arago, 75014 Paris (France) and Department of Mathematics and Applied Mathematics, Cape Town University, Rondebosch 7701 (South Africa) and National Institute for Theoretical Physics (NITheP), Stellenbosch 7600 (South Africa))
%J Living Reviews in Relativity, vol. 14, no. 2
%D 03/2011
%T Varying Constants, Gravitation and Cosmology
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2011-2
%I HTML: http://www.livingreviews.org/lrr-2011-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2011-2/download/lrr-2011-2Color.pdf; DOI: 10.1007/lrr-2011-2
%K fundamental physical constants, theoretical cosmology, general theory of gravitation
%B Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.
%R 2011LRR....14....3B
%A Barceló, Carlos; Liberati, Stefano; Visser, Matt
%F AA(Instituto de Astrofísica de Andalucía (CSIC), Camino Bajo de Huetor 50, 18008 Granada, Spain) AB(International School for Advanced Studies and INFN, Via Beirut 2-4, 34014 Trieste, Italy) AC(School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, PO Box 600, Wellington, New Zealand)
%J Living Reviews in Relativity, vol. 14, no. 3
%D 05/2011
%T Analogue Gravity
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2011-3
%I HTML: http://www.livingreviews.org/lrr-2011-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2011-3/download/lrr-2011-3Color.pdf; DOI: 10.1007/lrr-2011-3
%K Analogue gravity, Analog models, Gravity
%B Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).
%R 2011LRR....14....4A
%A Andréasson, Håkan
%F AA(Department of Mathematics, Chalmers University of Technology, S-41296 Göteborg, Sweden)
%J Living Reviews in Relativity, vol. 14, no. 4
%D 05/2011
%T The Einstein-Vlasov System/Kinetic Theory
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2011-4
%I HTML: http://www.livingreviews.org/lrr-2011-4; PDF: http://relativity.livingreviews.org/Articles/lrr-2011-4/download/lrr-2011-4Color.pdf; DOI: 10.1007/lrr-2011-4
%K Einstein-Vlasov system, Kinetic theory, Vlasov-Poisson system, Nordström-Vlasov system, Global existence
%B The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.
%R 2011LRR....14....5P
%A Pitkin, Matthew; Reid, Stuart; Rowan, Sheila; Hough, James
%F AA(Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K.) AB(Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K.) AC(Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K.) AD(Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K.)
%J Living Reviews in Relativity, vol. 14, no. 5
%D 07/2011
%T Gravitational Wave Detection by Interferometry (Ground and Space)
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2011-5
%I HTML: http://www.livingreviews.org/lrr-2011-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2011-5/download/lrr-2011-5Color.pdf; DOI: 10.1007/lrr-2011-5
%K Gravitational wave detectors, Gravitational waves, Laser interferometry, Data analysis, Science runs, Interferometric gravitational wave detectors, Noise sources
%B Significant progress has been made in recent years on the development of gravitational-wave detectors. Sources such as coalescing compact binary systems, neutron stars in low-mass X-ray binaries, stellar collapses and pulsars are all possible candidates for detection. The most promising design of gravitational-wave detector uses test masses a long distance apart and freely suspended as pendulums on Earth or in drag-free spacecraft. The main theme of this review is a discussion of the mechanical and optical principles used in the various long baseline systems in operation around the world - LIGO (USA), Virgo (Italy/France), TAMA300 and LCGT (Japan), and GEO600 (Germany/U.K.) - and in LISA, a proposed space-borne interferometer. A review of recent science runs from the current generation of ground-based detectors will be discussed, in addition to highlighting the astrophysical results gained thus far. Looking to the future, the major upgrades to LIGO (Advanced LIGO), Virgo (Advanced Virgo), LCGT and GEO600 (GEO-HF) will be completed over the coming years, which will create a network of detectors with the significantly improved sensitivity required to detect gravitational waves. Beyond this, the concept and design of possible future "third generation" gravitational-wave detectors, such as the Einstein Telescope (ET), will be discussed.
%R 2011LRR....14....6S
%A Shibata, Masaru; Taniguchi, Keisuke
%F AA(Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan) AB(Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan)
%J Living Reviews in Relativity, vol. 14, no. 6
%D 08/2011
%T Coalescence of Black Hole-Neutron Star Binaries
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2011-6
%I HTML: http://www.livingreviews.org/lrr-2011-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2011-6/download/lrr-2011-6Color.pdf; DOI: 10.1007/lrr-2011-6
%K neutron star, numerical relativity, black hole, gravitational waves
%B We review the current status of general relativistic studies for the coalescence of black hole-neutron star (BH-NS) binaries. First, procedures for a solution of BH-NS binaries in quasi-equilibrium circular orbits and the numerical results, such as quasi-equilibrium sequence and mass-shedding limit, of the high-precision computation, are summarized. Then, the current status of numerical-relativity simulations for the merger of BH-NS binaries is described. We summarize our understanding for the merger and/or tidal disruption processes, the criterion for tidal disruption, the properties of the remnant formed after the tidal disruption, gravitational waveform, and gravitational-wave spectrum.
%R 2011LRR....14....7P
%A Poisson, Eric; Pound, Adam; Vega, Ian
%F AA(Department of Physics, University of Guelph, Guelph, Ontario, Canada N1G 2W1 and Perimeter Institute for Theoretical Physics, 35 King Street North, Waterloo, Ontario, Canada N2J 2W9) AB(Department of Physics, University of Guelph, Guelph, Ontario, Canada N1G 2W1) AC(Department of Physics, University of Guelph, Guelph, Ontario, Canada N1G 2W1)
%J Living Reviews in Relativity, vol. 14, no. 7
%D 09/2011
%T The Motion of Point Particles in Curved Spacetime
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2011-7
%I HTML: http://www.livingreviews.org/lrr-2011-7; PDF: http://relativity.livingreviews.org/Articles/lrr-2011-7/download/lrr-2011-7Color.pdf; DOI: 10.1007/lrr-2011-7
%K self force, radiation reaction, equations of motion, point particles, electromagnetic field, scalar field, curved spacetime, gravitation
%B This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle.
The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle -- its only effect is to contribute to the particle's inertia. What remains after subtraction is a regular field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle; it is this interaction that gives rise to the self-force.
The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (Part II). It continues with a thorough discussion of Green's functions in curved spacetime (Part III). The review presents a detailed derivation of each of the three equations of motion (Part IV). Because the notion of a point mass is problematic in general relativity, the review concludes (Part V) with an alternative derivation of the equations of motion that applies to a small body of arbitrary internal structure.
%R 2011LRR....14....8S
%A Solodukhin, Sergey N.
%F AA(Laboratoire de Mathématiques et Physique Théorique, Université François-Rabelais Tours Fédération Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours, France)
%J Living Reviews in Relativity, vol. 14, no. 8
%D 10/2011
%T Entanglement Entropy of Black Holes
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2011-8
%I HTML: http://www.livingreviews.org/lrr-2011-8; PDF: http://relativity.livingreviews.org/Articles/lrr-2011-8/download/lrr-2011-8Color.pdf; DOI: 10.1007/lrr-2011-8
%K entanglement entropy, Bekenstein-Hawking entropy, black holes
%B The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the black-hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
%R 2012LRR....15....1A
%A Adamo, Timothy M.; Newman, Ezra T.; Kozameh, Carlos
%F AA(University of Oxford, Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB, U.K. ) AB(Department of Physics and Astronomy, University of Pittsburgh, U.S.A.) AC(Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Argentina)
%J Living Reviews in Relativity, vol. 15, no. 1
%D 01/2012
%T Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2012-1
%I HTML: http://www.livingreviews.org/lrr-2012-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-1/download/lrr-2012-1Color.pdf; DOI: 10.1007/lrr-2012-1
%K Shear-free congruences, H-space, Asymptotic flatness, Spin-coefficient formalism
%B A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues.
This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, ℋ-space. They in turn play a dominant role in the applications.
The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell) field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity.
More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum--conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.
%R 2012LRR....15....2W
%A Winicour, Jeffrey
%F AA(Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam-Golm, Germany and Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.)
%J Living Reviews in Relativity, vol. 15, no. 2
%D 01/2012
%T Characteristic Evolution and Matching
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2012-2
%I HTML: http://www.livingreviews.org/lrr-2012-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-2/download/lrr-2012-2Color.pdf; DOI: 10.1007/lrr-2012-2
%K Numerical relativity, Numerical methods, Characteristic initial value problem
%B I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D-axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black-hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black-hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.
%R 2012LRR....15....3S
%A Simón, Joan
%F AA(School of Mathematics, The University of Edinburgh, and Maxwell Institute for Mathematical Sciences, Edinburgh EH9 3JZ, U.K.)
%J Living Reviews in Relativity, vol. 15, no. 3
%D 02/2012
%T Brane Effective Actions, Kappa-Symmetry and Applications
%C (c) The author(s)
%G String Theory and Gravitation
%U http://www.livingreviews.org/lrr-2012-3
%I HTML: http://www.livingreviews.org/lrr-2012-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-3/download/lrr-2012-3Color.pdf; DOI: 10.1007/lrr-2012-3
%K Non-abelian gauge theories, Supersymmetry, AdS/CFT, Solitons, Kappa-symmetry
%B This is a review on brane effective actions, their symmetries and some of their applications. Its first part covers the Green–Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects: the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry to achieve manifest spacetime covariance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds.
Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as Bogomol’nyi–Prasad–Sommerfield (BPS) states carrying (topological) charges in the supersymmetry algebra and the connection between supersymmetry and Hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approximations to infer about the non-trivial dynamics of strongly-coupled gauge theories using the anti de Sitter/conformal field theory (AdS/CFT) correspondence. This includes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description.
Its final part briefly discusses effective actions for N D-branes and M2-branes. This includes both Super-Yang-Mills theories, their higher-order corrections and partial results in covariantising these couplings to curved backgrounds, and the more recent supersymmetric Chern–Simons matter theories describing M2-branes using field theory, brane constructions and 3-algebra considerations.
%R 2012LRR....15....4J
%A Jaranowski, Piotr; Królak, Andrzej
%F AA(Institute of Theoretical Physics, University of Białystok, Lipowa 41, 15-424 Białystok, Poland) AB(Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warsaw, Poland)
%J Living Reviews in Relativity, vol. 15, no. 4
%D 03/2012
%T Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2012-4
%I HTML: http://www.livingreviews.org/lrr-2012-4; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-4/download/lrr-2012-4Color.pdf; DOI: 10.1007/lrr-2012-4
%K parameter estimation, gravitational waves, signal detection
%B The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, ℱ-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.
%R 2012LRR....15....5D
%A Danilishin, Stefan L.; Khalili, Farid Ya.
%F AA(School of Physics, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia and Faculty of Physics, Moscow State University, Moscow 119991, Russia) AB(Faculty of Physics, Moscow State University, Moscow 119991, Russia)
%J Living Reviews in Relativity, vol. 15, no. 5
%D 04/2012
%T Quantum Measurement Theory in Gravitational-Wave Detectors
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2012-5
%I HTML: http://www.livingreviews.org/lrr-2012-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-5/download/lrr-2012-5Color.pdf; DOI: 10.1007/lrr-2012-5
%K quantum speed meter, back-action evasion, quantum measurement theory, quantum noise, standard quantum limit, quantum non-demolition measurement, gravitational-wave detectors, optical rigidity, squeezed light, filter cavities
%B The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.
%R 2012LRR....15....6L
%A Liebling, Steven L.; Palenzuela, Carlos
%F AA(Long Island University, Brookville, NY 11548, USA and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada) AB(Canadian Institute for Theoretical Astrophysics, Toronto, Ontario M5S 3H8, Canada)
%J Living Reviews in Relativity, vol. 15, no. 6
%D 05/2012
%T Dynamical Boson Stars
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2012-6
%I HTML: http://www.livingreviews.org/lrr-2012-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-6/download/lrr-2012-6Color.pdf; DOI: 10.1007/lrr-2012-6
%K Numerical relativity, Boson stars
%B The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s, John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called geons, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name boson stars. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single Killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.
%R 2012LRR....15....7C
%A Chruściel, Piotr T.; Costa, João; Heusler, Markus
%F AA(University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria) AB(Instituto Universitário de Lisboa (ISCTE-IUL), Lisboa, Portugal and Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal) AC(ITP, University of Zurich, CH-8057 Zurich, Switzerland)
%J Living Reviews in Relativity, vol. 15, no. 7
%D 05/2012
%T Stationary Black Holes: Uniqueness and Beyond
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2012-7
%I HTML: http://www.livingreviews.org/lrr-2012-7; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-7/download/lrr-2012-7Color.pdf; DOI: 10.1007/lrr-2012-7
%K uniqueness theorems, self-gravitating classical fields, black holes
%B The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.
%R 2012LRR....15....8F
%A Faber, Joshua A.; Rasio, Frederic A.
%F AA(Center for Computational Relativity and Gravitation and School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester NY 14623, USA) AB(Center for Interdisciplinary Exploration and Research in Astrophysics, and Department of Physics & Astronomy, Northwestern University, 2145 Sheridan Road, Evanston IL 60208, USA)
%J Living Reviews in Relativity, vol. 15, no. 8
%D 07/2012
%T Binary Neutron Star Mergers
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2012-8
%I HTML: http://www.livingreviews.org/lrr-2012-8; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-8/download/lrr-2012-8Color.pdf; DOI: 10.1007/lrr-2012-8
%K Numerical relativity, General relativity, Coalescing binaries, Neutron stars, Binary neutron stars
%B We review the current status of studies of the coalescence of binary neutron star systems. We begin with a discussion of the formation channels of merging binaries and we discuss the most recent theoretical predictions for merger rates. Next, we turn to the quasi-equilibrium formalisms that are used to study binaries prior to the merger phase and to generate initial data for fully dynamical simulations. The quasi-equilibrium approximation has played a key role in developing our understanding of the physics of binary coalescence and, in particular, of the orbital instability processes that can drive binaries to merger at the end of their lifetimes. We then turn to the numerical techniques used in dynamical simulations, including relativistic formalisms, (magneto-)hydrodynamics, gravitational-wave extraction techniques, and nuclear microphysics treatments. This is followed by a summary of the simulations performed across the field to date, including the most recent results from both fully relativistic and microphysically detailed simulations. Finally, we discuss the likely directions for the field as we transition from the first to the second generation of gravitational-wave interferometers and while supercomputers reach the petascale frontier.
%R 2012LRR....15....9S
%A Sarbach, Olivier; Tiglio, Manuel
%F AA(Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, 58040 Morelia, Michoacán, Mexico) AB(Center for Scientific Computation and Mathematical Modeling, Department of Physics, Joint Space Sciences Institute. Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA)
%J Living Reviews in Relativity, vol. 15, no. 9
%D 08/2012
%T Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations
%C (c) The author(s)
%G Mathematical Relativity
%U http://www.livingreviews.org/lrr-2012-9
%I HTML: http://www.livingreviews.org/lrr-2012-9; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-9/download/lrr-2012-9Color.pdf; DOI: 10.1007/lrr-2012-9
%K Boundary value problems, Partial differential equations
%B Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein's theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity.
The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein's equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.
%R 2012LRR....15...10F
%A Famaey, Benoît; McGaugh, Stacy S.
%F AA(Observatoire Astronomique de Strasbourg, CNRS, UMR 7550, France and AIfA, University of Bonn, Germany) AB(Department of Astronomy, University of Maryland, USA and Case Western Reserve University, USA)
%J Living Reviews in Relativity, vol. 15, no. 10
%D 09/2012
%T Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2012-10
%I HTML: http://www.livingreviews.org/lrr-2012-10; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-10/download/lrr-2012-10Color.pdf; DOI: 10.1007/lrr-2012-10
%K fundamental physics, Newtonian limit, astronomical observations, equations of motion, cosmology, extragalactic astronomy, theories of gravity, astrophysics
%B A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i) there is a vast amount of unseen mass in some novel form - dark matter - or (ii) the data indicate a breakdown of our understanding of dynamics on the relevant scales, or (iii) both. Here, we first review a few outstanding challenges for the dark matter interpretation of mass discrepancies in galaxies, purely based on observations and independently of any alternative theoretical framework. We then show that many of these puzzling observations are predicted by one single relation - Milgrom's law - involving an acceleration constant a_0 (or a characteristic surface density Σ_† = a_0∕G) on the order of the square-root of the cosmological constant in natural units. This relation can at present most easily be interpreted as the effect of a single universal force law resulting from a modification of Newtonian dynamics (MOND) on galactic scales. We exhaustively review the current observational successes and problems of this alternative paradigm at all astrophysical scales, and summarize the various theoretical attempts (TeVeS, GEA, BIMOND, and others) made to effectively embed this modification of Newtonian dynamics within a relativistic theory of gravity.
%R 2012LRR....15...11C
%A Compère, Geoffrey
%F AA(Physique Théorique et Mathématique, Université Libre de Bruxelles, CP 231, 1050 Bruxelles, Belgium)
%J Living Reviews in Relativity, vol. 15, no. 11
%D 10/2012
%T The Kerr/CFT Correspondence and its Extensions
%C (c) The author(s)
%G String Theory and Gravitation
%U http://www.livingreviews.org/lrr-2012-11
%I HTML: http://www.livingreviews.org/lrr-2012-11; PDF: http://relativity.livingreviews.org/Articles/lrr-2012-11/download/lrr-2012-11Color.pdf; DOI: 10.1007/lrr-2012-11
%K Black holes, AdS/CFT, holography, conformal field theory
%B We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner–Nordström black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an SL (2,ℤ) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr–Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.
%R 2013LRR....16....1A
%A Abramowicz, Marek A.; Fragile, P. Chris
%F AA(Physics Department, Göteborg University, SE-412-96 Göteborg, Sweden and N. Copernicus Astronomical Center, Bartycka 18, PL-00-716 Warszawa, Poland) AB(Department of Physics & Astronomy, College of Charleston, Charleston, SC 29424, USA)
%J Living Reviews in Relativity, vol. 16, no. 1
%D 01/2013
%T Foundations of Black Hole Accretion Disk Theory
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-2013-1
%I HTML: http://www.livingreviews.org/lrr-2013-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-1/download/lrr-2013-1Color.pdf; DOI: 10.1007/lrr-2013-1
%K black hole accretion disks
%B This review covers the main aspects of black hole accretion disk theory. We begin with the view that one of the main goals of the theory is to better understand the nature of black holes themselves. In this light we discuss how accretion disks might reveal some of the unique signatures of strong gravity: the event horizon, the innermost stable circular orbit, and the ergosphere. We then review, from a first-principles perspective, the physical processes at play in accretion disks. This leads us to the four primary accretion disk models that we review: Polish doughnuts (thick disks), Shakura-Sunyaev (thin) disks, slim disks, and advection-dominated accretion flows (ADAFs). After presenting the models we discuss issues of stability, oscillations, and jets. Following our review of the analytic work, we take a parallel approach in reviewing numerical studies of black hole accretion disks. We finish with a few select applications that highlight particular astrophysical applications: measurements of black hole mass and spin, black hole vs. neutron star accretion disks, black hole accretion disk spectral states, and quasi-periodic oscillations (QPOs).
%R 2013LRR....16....2H
%A Hossenfelder, Sabine
%F AA(Nordita, Roslagstullsbacken 23, 106 91 Stockholm, Sweden)
%J Living Reviews in Relativity, vol. 16, no. 2
%D 01/2013
%T Minimal Length Scale Scenarios for Quantum Gravity
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2013-2
%I HTML: http://www.livingreviews.org/lrr-2013-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-2/download/lrr-2013-2Color.pdf; DOI: 10.1007/lrr-2013-2
%K Minimal length, Quantum gravity, Generalized uncertainty principle
%B We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantum mechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantum mechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics.
%R 2013LRR....16....3P
%A Perez, Alejandro
%F AA(Centre de Physique Théorique Unité Mixte de Recherche (UMR 6207) du CNRS et des e Universités Aix-Marseille I, Aix-Marseille II, et du Sud Toulon-Var; laboratoire afilié a la FRUMAM (FR 2291))
%J Living Reviews in Relativity, vol. 16, no. 3
%D 02/2013
%T The Spin-Foam Approach to Quantum Gravity
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2013-3
%I HTML: http://www.livingreviews.org/lrr-2013-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-3/download/lrr-2013-3Color.pdf; DOI: 10.1007/lrr-2013-3
%K Quantum gravity
%B This article reviews the present status of the spin-foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently-introduced new models for four-dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self contained treatment of 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.
%R 2013LRR....16....4B
%A Benacquista, Matthew J.; Downing, Jonathan M. B.
%F AA(Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, TX, U.S.A.) AB(Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstraße 12-14, D-69120 Heidelberg, Germany)
%J Living Reviews in Relativity, vol. 16, no. 4
%D 03/2013
%T Relativistic Binaries in Globular Clusters
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-2013-4
%I HTML: http://www.livingreviews.org/lrr-2013-4; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-4/download/lrr-2013-4Color.pdf; DOI: 10.1007/lrr-2013-4
%K Gravitational wave sources, Binary systems, Black holes, Globular clusters, Pulsars, Accretion disks
%B Galactic globular clusters are old, dense star systems typically containing 10^4 – 10^6 stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution that leads to relativistic binaries, and current and possible future observational evidence for this population. Our discussion of globular cluster evolution will focus on the processes that boost the production of tight binary systems and the subsequent interaction of these binaries that can alter the properties of both bodies and can lead to exotic objects. Direct N-body integrations and Fokker–Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.
%R 2013LRR....16....5A
%A Amelino-Camelia, Giovanni
%F AA(Dipart. Fisica Univ. La Sapienza and Sez. Roma1 INFN, P.le Moro 2, I-00185 Roma, Italy)
%J Living Reviews in Relativity, vol. 16, no. 5
%D 06/2013
%T Quantum-Spacetime Phenomenology
%C (c) The author(s)
%G Quantum General Relativity
%U http://www.livingreviews.org/lrr-2013-5
%I HTML: http://www.livingreviews.org/lrr-2013-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-5/download/lrr-2013-5Color.pdf; DOI: 10.1007/lrr-2013-5
%K Loop quantum gravity, Quantum spacetime, Spacetime noncommutativity
%B I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. My main focus is on phenomenological programs that affect the directions taken by studies of quantum-spacetime theories.
%R 2013LRR....16....6A
%A Amendola, Luca; Group, Euclid Theory Working
%F AA(Institut für Theoretische Physik, Philosophenweg 16, D-69120 Heidelberg) AB()
%J Living Reviews in Relativity, vol. 16, no. 6
%D 09/2013
%T Cosmology and Fundamental Physics with the Euclid Satellite
%C (c) The author(s)
%G Physical Cosmology
%U http://www.livingreviews.org/lrr-2013-6
%I HTML: http://www.livingreviews.org/lrr-2013-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-6/download/lrr-2013-6Color.pdf; DOI: 10.1007/lrr-2013-6
%K cosmology, galaxy evolution, dark energy
%B Euclid is a European Space Agency medium-class mission selected for launch in 2019 within the Cosmic Vision 2015-2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky.
Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis.
This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.
%R 2013LRR....16....7G
%A Gair, Jonathan R.; Vallisneri, Michele; Larson, Shane L.; Baker, John G.
%F AA(Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, UK) AB(Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA) AC(Center for Interdisclipinary Research and Exploration in Astrophysics, Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA) AD(Gravitational Astrophysics Lab, NASA Goddard Space Flight Center, 8800 Greenbelt Rd., Greenbelt, MD 20771, USA)
%J Living Reviews in Relativity, vol. 16, no. 7
%D 09/2013
%T Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2013-7
%I HTML: http://www.livingreviews.org/lrr-2013-7; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-7/download/lrr-2013-7Color.pdf; DOI: 10.1007/lrr-2013-7
%K gravitational waves, black holes, general relativity, data analysis, eLISA, LISA, gravitation
%B We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ∼ 10^{-5} – 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger.
%R 2013LRR....16....8K
%A Kunduri, Hari K.; Lucietti, James
%F AA(Department of Mathematics and Statistics, Memorial University of Newfoundland, St John's NL A1C 4P5, Canada) AB(School of Mathematics and Maxwell Institute of Mathematical Sciences, University of Edinburgh, King's Buildings, Edinburgh, EH9 3JZ, UK)
%J Living Reviews in Relativity, vol. 16, no. 8
%D 09/2013
%T Classification of Near-Horizon Geometries of Extremal Black Holes
%C (c) The author(s)
%G String Theory and Gravitation
%U http://www.livingreviews.org/lrr-2013-8
%I HTML: http://www.livingreviews.org/lrr-2013-8; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-8/download/lrr-2013-8Color.pdf; DOI: 10.1007/lrr-2013-8
%K Extremal black holes, Black holes, Near-horizon geometry
%B Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein–Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.
%R 2013LRR....16....9Y
%A Yunes, Nicolás; Siemens, Xavier
%F AA(Department of Physics, Montana State University, Bozeman, MO 59717, USA) AB(Center for Gravitation, Cosmology, and Astrophysics, Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA)
%J Living Reviews in Relativity, vol. 16, no. 9
%D 11/2013
%T Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2013-9
%I HTML: http://www.livingreviews.org/lrr-2013-9; PDF: http://relativity.livingreviews.org/Articles/lrr-2013-9/download/lrr-2013-9Color.pdf; DOI: 10.1007/lrr-2013-9
%K Alternative theories, Compact binaries, Observational tests, Pulsar timing, Gravitational waves, General relativity, Experimental tests
%B This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.
%R 2014LRR....17....1S
%A Stachel, John
%F AA(Center for Einstein Studies, Boston University, 745 Commonwealth Avenue, Boston, MA 02215, U.S.A.)
%J Living Reviews in Relativity, vol. 17, no. 1
%D 02/2014
%T The Hole Argument and Some Physical and Philosophical Implications
%C (c) The author(s)
%G History of Relativity
%U http://www.livingreviews.org/lrr-2014-1
%I HTML: http://www.livingreviews.org/lrr-2014-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2014-1/download/lrr-2014-1Color.pdf; DOI: 10.1007/lrr-2014-1
%K Philosophy of science, General relativity, History of science
%B This is a historical-critical study of the hole argument, concentrating on the interface between historical, philosophical and physical issues. Although it includes a review of its history, its primary aim is a discussion of the contemporary implications of the hole argument for physical theories based on dynamical, background-independent space-time structures.
The historical review includes Einstein’s formulations of the hole argument, Kretschmann’s critique, as well as Hilbert’s reformulation and Darmois’ formulation of the general-relativistic Cauchy problem. The 1970s saw a revival of interest in the hole argument, growing out of attempts to answer the question: Why did three years elapse between Einstein’s adoption of the metric tensor to represent the gravitational field and his adoption of the Einstein field equations?
The main part presents some modern mathematical versions of the hole argument, including both coordinate-dependent and coordinate-independent definitions of covariance and general covariance; and the fiber bundle formulation of both natural and gauge natural theories. By abstraction from continuity and differentiability, these formulations can be extended from differentiable manifolds to any set; and the concepts of permutability and general permutability applied to theories based on relations between the elements of a set, such as elementary particle theories.
We are closing with an overview of current discussions of philosophical and physical implications of the hole argument.
%R 2014LRR....17....2B
%A Blanchet, Luc
%F AA(Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France)
%J Living Reviews in Relativity, vol. 17, no. 2
%D 02/2014
%T Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2014-2
%I HTML: http://www.livingreviews.org/lrr-2014-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2014-2/download/lrr-2014-2Color.pdf; DOI: 10.1007/lrr-2014-2
%K Gravitational radiation, Post-Newtonian approximations, Inspiralling compact binary, Multipolar expansion
%B To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries -- binary star systems composed of neutron stars and/or black holes in their late stage of evolution -- require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary's orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries -- moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.
%R 2014LRR....17....3P
%A Postnov, Konstantin A.; Yungelson, Lev R.
%F AA(Moscow M.V. Lomonosov State University, Sternberg Astronomical Institute, 13 Universitetskij Pr., 119992 Moscow, Russia) AB(Institute of Astronomy of the Russian Academy of Sciences, 48 Pyatnitskaya Str., 119017 Moscow, Russia)
%J Living Reviews in Relativity, vol. 17, no. 3
%D 05/2014
%T The Evolution of Compact Binary Star Systems
%C (c) The author(s)
%G Relativity in Astrophysics
%U http://www.livingreviews.org/lrr-2014-3
%I HTML: http://www.livingreviews.org/lrr-2014-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2014-3/download/lrr-2014-3Color.pdf; DOI: 10.1007/lrr-2014-3
%K AM CVn stars, Supernovae, Binary systems, Black holes, Neutron stars, White dwarfs, Gravitational-wave sources, Astrophysics
%B We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Mergings of compact-star binaries are expected to be the most important sources for forthcoming gravitational-wave (GW) astronomy. In the first part of the review, we discuss observational manifestations of close binaries with NS and/or BH components and their merger rate, crucial points in the formation and evolution of compact stars in binary systems, including the treatment of the natal kicks, which NSs and BHs acquire during the core collapse of massive stars and the common envelope phase of binary evolution, which are most relevant to the merging rates of NS-NS, NS-BH and BH-BH binaries. The second part of the review is devoted mainly to the formation and evolution of binary WDs and their observational manifestations, including their role as progenitors of cosmologically-important thermonuclear SN Ia. We also consider AM CVn-stars, which are thought to be the best verification binary GW sources for future low-frequency GW space interferometers.
%R 2014LRR....17....4W
%A Will, Clifford M.
%F AA(Department of Physics, University of Florida, Gainesville FL 32611)
%J Living Reviews in Relativity, vol. 17, no. 4
%D 06/2014
%T The Confrontation between General Relativity and Experiment
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2014-4
%I HTML: http://www.livingreviews.org/lrr-2014-4; PDF: http://relativity.livingreviews.org/Articles/lrr-2014-4/download/lrr-2014-4Color.pdf; DOI: 10.1007/lrr-2014-4
%K Gravitational radiation, Tests of relativistic gravity, Theories of gravity, Post-Newtonian limit
%B The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse–Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.
%R 2014LRR....17....5G
%A Goenner, Hubert F. M.
%F AA(University of Göttingen, Institut für Theoretische Physik, Tammannstr. 1, D-37077 Göttingen, Germany)
%J Living Reviews in Relativity, vol. 17, no. 5
%D 06/2014
%T On the History of Unified Field Theories. Part II. (ca. 1930 – ca. 1965)
%C (c) The author(s)
%G History of Relativity
%U http://www.livingreviews.org/lrr-2014-5
%I HTML: http://www.livingreviews.org/lrr-2014-5; PDF: http://relativity.livingreviews.org/Articles/lrr-2014-5/download/lrr-2014-5Color.pdf; DOI: 10.1007/lrr-2014-5
%K Unified field theory, History of science, Differential geometry
%B The present review intends to provide an overall picture of the research concerning classical unified field theory, worldwide, in the decades between the mid-1930 and mid-1960. Main themes are the conceptual and methodical development of the field, the interaction among the scientists working in it, their opinions and interpretations. Next to the most prominent players, A. Einstein and E. Schrödinger, V. Hlavatý and the French groups around A. Lichnerowicz, M.-A. Tonnelat, and Y. Thiry are presented. It is shown that they have given contributions of comparable importance. The review also includes a few sections on the fringes of the central topic like Born–Infeld electromagnetic theory or scalar-tensor theory. Some comments on the structure and organization of research-groups are also made.
%R 2014LRR....17....6T
%A Tinto, Massimo; Dhurandhar, Sanjeev V.
%F AA(Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, U.S.A. and LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, U.S.A.) AB(IUCAA, Post Bag 4, Ganeshkhind, Pune 411 007, India)
%J Living Reviews in Relativity, vol. 17, no. 6
%D 08/2014
%T Time-Delay Interferometry
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2014-6
%I HTML: http://www.livingreviews.org/lrr-2014-6; PDF: http://relativity.livingreviews.org/Articles/lrr-2014-6/download/lrr-2014-6Color.pdf; DOI: 10.1007/lrr-2014-6
%K Gravitational-wave detectors, Interferometry
%B Equal-arm detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set the overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector. In order to solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called time-delay interferometry (TDI).
This article provides an overview of the theory, mathematical foundations, and experimental aspects associated with the implementation of TDI. Although emphasis on the application of TDI to the Laser Interferometer Space Antenna (LISA) mission appears throughout this article, TDI can be incorporated into the design of any future space-based mission aiming to search for gravitational waves via interferometric measurements. We have purposely left out all theoretical aspects that data analysts will need to account for when analyzing the TDI data combinations.
%R 2014LRR....17....7D
%A de Rham, Claudia
%F AA(CERCA & Physics Department, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106, USA)
%J Living Reviews in Relativity, vol. 17, no. 7
%D 08/2014
%T Massive Gravity
%C (c) The author(s)
%G Experimental Foundations of Gravitation
%U http://www.livingreviews.org/lrr-2014-7
%I HTML: http://www.livingreviews.org/lrr-2014-7; PDF: http://relativity.livingreviews.org/Articles/lrr-2014-7/download/lrr-2014-7Color.pdf; DOI: 10.1007/lrr-2014-7
%K General relativity, Gravity, Alternative theories of gravity, Modified theories of gravity, Massive gravity
%B We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali–Gabadadze–Porrati model (DGP), cascading gravity, and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware–Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally, we present alternative and related models of massive gravity such as new massive gravity, Lorentz-violating massive gravity and non-local massive gravity.
%R 2015LRR....18....1C
%A Cardoso, Vítor; Gualtieri, Leonardo; Herdeiro, Carlos A. R.; Sperhake, Ulrich
%F AA(CENTRA, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada) AB(Dipartimento di Fisica, Università di Roma “La Sapienza” & Sezione INFN Roma1, P.A. Moro 5, 00185, Roma, Italy) AC(Departamento de Física da Universidade de Aveiro and CIDMA, Campus de Santiago, 3810-183 Aveiro, Portugal) AD(DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K.)
%J Living Reviews in Relativity, vol. 18, no. 1
%D 09/2015
%T Exploring New Physics Frontiers Through Numerical Relativity
%C (c) The author(s)
%G Numerical Relativity
%U http://www.livingreviews.org/lrr-2015-1
%I HTML: http://www.livingreviews.org/lrr-2015-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2015-1/download/lrr-2015-1Color.pdf; DOI: 10.1007/lrr-2015-1
%K Numerical methods, Extra dimensions, Black holes, Gravitation, Extensions of the standard model, Trans-Planckian scattering, Alternative theories of gravity
%B The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein’s equations – along with some spectacular results – in various setups.
We review techniques for solving Einstein’s equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.
%R 2015LRR....18....2J
%A Jackson, Neal
%F AA(Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Turing Building, Manchester M13 9PL, U.K.)
%J Living Reviews in Relativity, vol. 18, no. 2
%D 09/2015
%T The Hubble Constant
%C (c) The author(s)
%G Physical Cosmology
%U http://www.livingreviews.org/lrr-2015-2
%I HTML: http://www.livingreviews.org/lrr-2015-2; PDF: http://relativity.livingreviews.org/Articles/lrr-2015-2/download/lrr-2015-2Color.pdf; DOI: 10.1007/lrr-2015-2
%K Hubble constant, Cosmology
%B I review the current state of determinations of the Hubble constant, which gives the length scale of the Universe by relating the expansion velocity of objects to their distance. There are two broad categories of measurements. The first uses individual astrophysical objects which have some property that allows their intrinsic luminosity or size to be determined, or allows the determination of their distance by geometric means. The second category comprises the use of all-sky cosmic microwave background, or correlations between large samples of galaxies, to determine information about the geometry of the Universe and hence the Hubble constant, typically in a combination with other cosmological parameters. Many, but not all, object-based measurements give H_0 values of around 72–74 km s^–1 Mpc^–1, with typical errors of 2–3 km s^–1 Mpc^–1. This is in mild discrepancy with CMB-based measurements, in particular those from the Planck satellite, which give values of 67–68 km s^–1 Mpc^–1 and typical errors of 1–2 km s^–1 Mpc^–1. The size of the remaining systematics indicate that accuracy rather than precision is the remaining problem in a good determination of the Hubble constant. Whether a discrepancy exists, and whether new physics is needed to resolve it, depends on details of the systematics of the object-based methods, and also on the assumptions about other cosmological parameters and which datasets are combined in the case of the all-sky methods.
%R 2015LRR....18....3H
%A Harms, Jan
%F AA(Università degli Studi di Urbino ‘Carlo Bo’, 61029 Urbino, Italy)
%J Living Reviews in Relativity, vol. 18, no. 3
%D 12/2015
%T Terrestrial Gravity Fluctuations
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2015-3
%I HTML: http://www.livingreviews.org/lrr-2015-3; PDF: http://relativity.livingreviews.org/Articles/lrr-2015-3/download/lrr-2015-3Color.pdf; DOI: 10.1007/lrr-2015-3
%K Terrestrial gravity, Newtonian noise, Wiener filter, Mitigation
%B Different forms of fluctuations of the terrestrial gravity field are observed by gravity experiments. For example, atmospheric pressure fluctuations generate a gravity-noise foreground in measurements with super-conducting gravimeters. Gravity changes caused by high-magnitude earthquakes have been detected with the satellite gravity experiment GRACE, and we expect high-frequency terrestrial gravity fluctuations produced by ambient seismic fields to limit the sensitivity of ground-based gravitational-wave (GW) detectors. Accordingly, terrestrial gravity fluctuations are considered noise and signal depending on the experiment. Here, we will focus on ground-based gravimetry. This field is rapidly progressing through the development of GW detectors. The technology is pushed to its current limits in the advanced generation of the LIGO and Virgo detectors, targeting gravity strain sensitivities better than 10^–23 Hz^–1/2 above a few tens of a Hz. Alternative designs for GW detectors evolving from traditional gravity gradiometers such as torsion bars, atom interferometers, and superconducting gradiometers are currently being developed to extend the detection band to frequencies below 1 Hz. The goal of this article is to provide the analytical framework to describe terrestrial gravity perturbations in these experiments. Models of terrestrial gravity perturbations related to seismic fields, atmospheric disturbances, and vibrating, rotating or moving objects, are derived and analyzed. The models are then used to evaluate passive and active gravity noise mitigation strategies in GW detectors, or alternatively, to describe their potential use in geophysics. The article reviews the current state of the field, and also presents new analyses especially with respect to the impact of seismic scattering on gravity perturbations, active gravity noise cancellation, and time-domain models of gravity perturbations from atmospheric and seismic point sources. Our understanding of terrestrial gravity fluctuations will have great impact on the future development of GW detectors and high-precision gravimetry in general, and many open questions need to be answered still as emphasized in this article.
%R 2016LRR....19....1A
%A Abbott, Benjamin P.; Collaboration, LIGO Scientific; Collaboration, Virgo
%F AA(California Institute of Technology, Pasadena, U.S.A.) AB() AC()
%J Living Reviews in Relativity, vol. 19, no. 1
%D 02/2016
%T Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO and Advanced Virgo
%C (c) The author(s)
%G Gravitational Waves
%U http://www.livingreviews.org/lrr-2016-1
%I HTML: http://www.livingreviews.org/lrr-2016-1; PDF: http://relativity.livingreviews.org/Articles/lrr-2016-1/download/lrr-2016-1Color.pdf; DOI: 10.1007/lrr-2016-1
%K Data analysis, Gravitational-wave detectors, Gravitational waves, Electromagnetic counterparts
%B We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 deg^2 to 20 deg^2 will require at least three detectors of sensitivity within a factor of ~2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.