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.

Figure 1

Results for the binding energy E_ICO versus ω_ICO in the equal-mass case (ν = 1/4). The asterisk marks the result calculated by numerical relativity. The points indicated by 1PN, 2PN, and 3PN are computed from the minimum of Equation (194), and correspond to irrotational binaries. The points denoted by 1PN^corot, 2PN^corot, and 3PN^corot come from the minimum of the sum of Equations (194) and (202), and describe corotational binaries.