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4.2 Motion and gravitational radiation in general relativity

The motion of bodies and the generation of gravitational radiation are long-standing problems that date back to the first years following the publication of GR, when Einstein calculated the gravitational radiation emitted by a laboratory-scale object using the linearized version of GR, and de Sitter calculated N-body equations of motion for bodies in the 1PN approximation to GR. It has at times been controversial, with disputes over such issues as whether Einstein’s equations alone imply equations of motion for bodies (Einstein, Infeld, and Hoffman demonstrated explicitly that they do, using a matching procedure similar to the one described above), whether gravitational waves are real or are artifacts of general covariance (Einstein waffled; Bondi and colleagues proved their reality rigorously in the 1950s), and even over algebraic errors (Einstein erred by a factor of 2 in his first radiation calculation; Eddington found the mistake). Shortly after the discovery of the binary pulsar PSR 1913+16 in 1974, questions were raised about the foundations of the “quadrupole formula” for gravitational radiation damping (and in some quarters, even about its quantitative validity). These questions were answered in part by theoretical work designed to shore up the foundations of the quadrupole approximation, and in part (perhaps mostly) by the agreement between the predictions of the quadrupole formula and the observed rate of damping of the pulsar’s orbit (see Section 5.1). Damour [70Jump To The Next Citation Point] gives a thorough historical and technical review of this subject up to 1986.

The problem of motion and radiation in GR has received renewed interest since 1990, with proposals for construction of large-scale laser interferometric gravitational wave observatories, such as the LIGO project in the US, VIRGO and GEO600 in Europe, and TAMA300 in Japan, and the realization that a leading candidate source of detectable waves would be the inspiral, driven by gravitational radiation damping, of a binary system of compact objects (neutron stars or black holes) [1Jump To The Next Citation Point256Jump To The Next Citation Point]. The analysis of signals from such systems will require theoretical predictions from GR that are extremely accurate, well beyond the leading-order prediction of Newtonian or even post-Newtonian gravity for the orbits, and well beyond the leading-order formulae for gravitational waves.

This presented a major theoretical challenge: to calculate the motion and radiation of systems of compact objects to very high PN order, a formidable algebraic task, while addressing a number of issues of principle that have historically plagued this subject, sufficiently well to ensure that the results were physically meaningful. This challenge has been largely met, so that we may soon see a remarkable convergence between observational data and accurate predictions of gravitational theory that could provide new, strong-field tests of GR.

Here we give a brief overview of the problem of motion and gravitational radiation in GR.

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