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
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