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Part B: Compact Binary Systems

The problem of the motion and gravitational radiation of compact objects in post-Newtonian approximations of general relativity is of crucial importance, for at least three reasons. First, the motion of N objects at the 1PN level (1/c2), according to the Einstein-Infeld-Hoffmann equations [106Jump To The Next Citation Point], is routinely taken into account to describe the Solar System dynamics (see Ref. [163]). Second, the gravitational radiation-reaction force, which appears in the equations of motion at the 2.5PN order, has been experimentally verified, by the observation of the secular acceleration of the orbital motion of the binary pulsar PSR 1913+16 [208209207].

Last but not least, the forthcoming detection and analysis of gravitational waves emitted by inspiralling compact binaries - two neutron stars or black holes driven into coalescence by emission of gravitational radiation - will necessitate the prior knowledge of the equations of motion and radiation field up to high post-Newtonian order. As discussed in the introduction in Section 1 (see around Equations (6View Equation, 7View Equation, 8View Equation)), the appropriate theoretical description of inspiralling compact binaries is by two structureless point-particles, characterized solely by their masses m1 and m2 (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. Several analyses [77Jump To The Next Citation Point78Jump To The Next Citation Point11179Jump To The Next Citation Point203183Jump To The Next Citation Point184Jump To The Next Citation Point152Jump To The Next Citation Point92Jump To The Next Citation Point93Jump To The Next Citation Point59Jump To The Next Citation Point58Jump To The Next Citation Point91Jump To The Next Citation Point16] have shown that, in order to get sufficiently accurate theoretical templates, one must include post-Newtonian effects up to the 3PN level at least.

To date, the templates have been completed through 3.5PN order for the phase evolution [35Jump To The Next Citation Point40Jump To The Next Citation Point31Jump To The Next Citation Point], and 2.5PN order for the amplitude corrections [46Jump To The Next Citation Point4Jump To The Next Citation Point]. Spin effects are known for the dominant relativistic spin-orbit coupling term at 1.5PN order and the spin-spin coupling term at 2PN order [146Jump To The Next Citation Point3144Jump To The Next Citation Point11911811770], and also for the next-to-leading spin-orbit coupling at 2.5PN order [168Jump To The Next Citation Point204Jump To The Next Citation Point110Jump To The Next Citation Point25Jump To The Next Citation Point]. Update

8 Regularization of the Field of Point Particles
9 Newtonian-like Equations of Motion
10 Gravitational Waves from Compact Binaries

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