Part B
Compact Binary Systems

The problem of the motion and gravitational radiation of compact objects in post-Newtonian approximations is of crucial importance, for at least three reasons listed in the Introduction of this article: Motion of N planets in the solar system; gravitational radiation reaction force in binary pulsars; direct detection of gravitational waves from inspiralling compact binaries. As discussed in Section 1.3, the appropriate theoretical description of inspiralling compact binaries is by two structureless point-particles, characterized solely by their masses and (and possibly their spins), and moving on a quasi-circular orbit.

Strategies to detect and analyze the very weak signals from compact binary inspiral involve matched filtering of a set of accurate theoretical template waveforms against the output of the detectors. Many analyses [139*, 137*, 198, 138*, 393*, 346*, 350*, 284*, 157*, 158*, 159*, 156*, 105*, 106*, 3*, 18*, 111*] have shown that, in order to get sufficiently accurate theoretical templates, one must include post-Newtonian effects up to the 3PN level or higher. Recall that in practice, the post-Newtonian templates for the inspiral phase have to be matched to numerical-relativity results for the subsequent merger and ringdown phases. The match proceeds essentially through two routes: Either the so-called Hybrid templates obtained by direct matching between the PN expanded waveform and the numerical computations [4, 371], or the Effective-One-Body (EOB) templates [108, 109, 161*, 168] that build on post-Newtonian results and extend their realm of validity to facilitate the analytical comparison with numerical relativity [112, 329]. Note also that various post-Newtonian resummation techniques, based on Padé approximants, have been proposed to improve the efficiency of PN templates [157, 158, 161].