Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

TL;DR

This paper reviews the theoretical framework for gravitational wave emission from isolated systems, focusing on post-Newtonian approximations and their application to inspiralling compact binaries, including detailed equations and energy flux calculations.

Contribution

It provides explicit expressions for source multipole moments and extends gravitational-wave energy flux calculations to 3.5PN order for binary systems.

Findings

Derived binary equations of motion at 3PN order.

Calculated gravitational-wave energy flux up to 3.5PN order.

Analyzed the orbital phase evolution for inspiralling 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 non-linear 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.