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.
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 French XVIIIth century as l’analyse sublime: the analytical method, and the resolution of partial differential equations
For general sources it is hopeless to solve the problem via a rigorous deduction within the exact theory of general relativity, and we have to resort to approximation methods, keeping in mind that, sadly, such methods are often not related in a very precise mathematical way to the first principles of the theory
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries 11 a substantial role. This expectation has been confirmed in recent years by several measurementanalyses [48, 49, 72, 50, 135, 121, 122, 96, 59], which have demonstrated that the post-Newtonian precision needed to implement successively the optimal filtering technique in 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
Summary
This fast-track revision incorporates the changes in some equations following the Errata to be published in Phys. Page 65: Equation 165 corrected Page 65: Equation corrected Page 65: Equation corrected Page 66: Equation corrected Page 66: Equation corrected Page 66: Equation corrected
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