Second-post-Newtonian generation of gravitational radiation

This paper derives the expressions of the multipole moments of an isolated gravitating source with an accuracy corresponding to the second-post-Newtonian (2PN) approximation of general relativity. The moments are obtained by a procedure of matching 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 in 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 2PN 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.