eng
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Living Reviews in Relativity
1433-8351
2012-01-23
15
1
10.12942/lrr-2012-1
lrr-2012-1
article
Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Timothy M. Adamo
1
Ezra T. Newman
2
Carlos Kozameh
3
University of Oxford, Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB, U.K.
Department of Physics and Astronomy, University of Pittsburgh, U.S.A.
Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Argentina
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.
http://www.livingreviews.org/lrr-2012-1
H-space
Asymptotic flatness
Shear-free congruences
Spin-coefficient formalism