Second-post-Newtonian generation of gravitational radiation

TL;DR

This work advances the analytic description of gravitational radiation by deriving the source multipole moments at the second post-Newtonian ($2$-PN) level within a multipolar-post-Minkowskian framework. It achieves this through a rigorous matching of the internal near-zone metric to the exterior canonical field, expressing the moments as finite, regularized integrals over the matter and gravitational-field content. The authors relate the canonical moments to the physical source moments $I_L$ and $J_L$, incorporate tail effects, and derive the $2$-PN asymptotic waveform and energy flux via radiative moments $U_L$ and $V_L$. The results lay groundwork for precise gravitational-wave templates for detectors like LIGO and VIRGO, and anticipate application to coalescing compact binaries in a forthcoming study.

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.