Second-post-Newtonian generation of gravitational radiation

TL;DR

This paper derives second post-Newtonian multipole moments for isolated gravitating sources, enabling more accurate modeling of gravitational waves for future detector observations.

Contribution

It provides the first detailed derivation of 2-PN multipole moments and their use in calculating gravitational waveforms and energy emission.

Findings

Derived 2-PN multipole moments from matter and gravitational fields.

Expressed the gravitational waveform and energy at 2-PN accuracy.

Moments are mathematically well-defined with compact support.

Abstract

This paper derives the expressions of the multipole moments of an isolated gravitating source with an accuracy corresponding to the second post-Newtonian (2-PN) approximation of general relativity. The moments are obtained by a procedure of matching of the external gravitational field of the source to the inner field, and are found to be given by integrals extending over the stress-energy distribution of the matter fields and the gravitational field. Although this is not manifest on their expressions, the moments have a compact support limited to the material source only (they are thus perfectly well-defined mathematically). From the multipole moments we deduce the expressions of the asymptotic gravitational waveform and associated energy generated by the source at the 2-PN approximation. This work, together with a forthcoming work devoted to the application to coalescing compact binaries, will be used in the future observations of gravitational radiation by laser interferometric detectors.