Abstract
To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries — binary star systems composed of neutron stars and/or black holes in their late stage of evolution — require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary’s orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries — moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.
Highlights
The theory of gravitational radiation from isolated sources, in the context of general relativity, is a fascinating science that can be explored by means of what was referred to in the XVIIIth century France as l’analyse sublime: The analytical method, and the resolution of partial differential equations
Inspiralling compact binaries are ideally suited for application of a high-order post-Newtonian wave generation formalism. These systems are very relativistic, with orbital velocities as high as 0.5c in the last rotations, so it is not surprising that the quadrupole-moment formalism (2) – (6) constitutes a poor description of the emitted gravitational waves, since many post-Newtonian corrections are expected to play a substantial role. This expectation has been confirmed by measurement-analyses [139, 137, 198, 138, 393, 346, 350, 284, 157], which have demonstrated that the post-Newtonian precision needed to implement successfully the optimal filtering technique for the LIGO/VIRGO detectors corresponds grossly, in the case of neutron-star binaries, to the 3PN approximation, or 1/c6 beyond the quadrupole moment approximation
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
Summary
Major revision, updated and expanded. About 180 new references. Improved introduction with added Section 1.2 on quadrupole formalism; More extensive description of asymptotic waveform and relation between radiative and source moments (Section 3.3); More complete discussion on radiation reaction effects (5.2) and explicit radiation reaction potentials (5.4); New Section 7.5 on the PN metric in the near zone; New sections on conservative dynamics: stability of orbits (8.2), first law of binary dynamics (8.3), comparison with self-force computations (8.4); New Section 9.5 on spherical-harmonic modes of gravitational waves; New sections on eccentric binaries: structure of the motion (10.1), quasi-Keplerian representation (10.2), averaged fluxes (10.3); New sections on spin effects: Lagrangian formalism (11.1), equations of motion (11.2), spin-orbit terms in the phase (11.3).
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