Gravitational Radiation from PostNewtonian Sources and Inspiralling Compact Binaries
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 highaccuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a highorder postNewtonian gravitational wave generation formalism. In this article, we present the current state of the art on postNewtonian 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 postNewtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the selffield regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the postNewtonian approximation and make a comparison with numerical computations of the gravitational selfforce for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high postNewtonian 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 quasielliptical orbits with nonnegligible 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 postNewtonian order (restricting to spinorbit effects which are linear in spins), and analyze the postNewtonian spin precession equations as well as the induced precession of the orbital plane.
 Publication:

Living Reviews in Relativity
 Pub Date:
 December 2014
 DOI:
 10.12942/lrr20142
 arXiv:
 arXiv:1310.1528
 Bibcode:
 2014LRR....17....2B
 Keywords:

 PostNewtonian approximation;
 Gravitational radiation;
 Multipolar expansion;
 Inspiralling compact binary;
 PostNewtonian approximations;
 General Relativity and Quantum Cosmology
 EPrint:
 185 pages, 5 figures, 428 references