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 (6, 7, 8)), 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. Several analyses [77, 78, 111, 79, 203, 183, 184, 152, 92, 93, 59, 58, 91, 1, 6] 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 [35, 40, 31], and 2.5PN order for the amplitude corrections [46, 4]. 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 [146, 3, 144, 119, 118, 117, 70], and also for the next-to-leading spin-orbit coupling at 2.5PN order [168, 204, 110, 25]. 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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