### 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 [70] 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) [1, 256]. 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.