Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Abstract

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

Effect of massive perturbers on extreme mass-ratio inspiral waveforms

“…As is expected, all propagation effects, such as the backscattering (or tails) of GWs off the metric of the secondary SMBH, occur beyond Newtonian (leading) order in post-Newtonian theory [36], and can be safely neglected here. The presence of an external source, however, does introduce non-negligible modifications to the generation of GWs.…”

Sources of Gravitational Waves: Theory and Observations

“…The reader is referred to the original articles, reviews [72][73][74][75][76][77] and books [78][79][80][81] for more details.…”

“…The radiative coordinate system X µ can be related to the source-rooted coordinate system x µ = (c t, x) [73]. The source quadrupole moment at Newtonian order is…”

“…We indicate with n/2-PN the PN term of formal order O(1/c n ) relative to the leading non-spinning term 4 . (For PN results of highly eccentric systems the reader may consult [73] and references therein. )…”

Stability of the puncture method with a generalized Baumgarte-Shapiro-Shibata-Nakamura formulation

“…The inspiraling phase of a binary black-hole (BBH) prior to merger as well as the ringdown phase after the merger can be modeled accurately by the approximate post-Newtonian [11] and perturbation methods [12], respectively. In order to simulate the late inspiral and merger of a BBH, however, numerical methods are required to solve the fully non-linear Einstein equations.…”