Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order

• Published in: Classical and quantum gravity Vol. 32; no. 4; pp. 45016 - 45052
• Main Authors: Faye, Guillaume, Blanchet, Luc, Iyer, Bala R
• Format: Journal Article
• Language: English
• Published: IOP Publishing 19.02.2015
• Subjects: Approximation; black holes; Couplings; Gravitational waves; Multipoles; neutron stars; Nonlinearity; perturbation theory; post-Newtonian approximation; Quadrupoles; Quantum gravity; related approximations; Waveforms
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/0264-9381/32/4/045016

This paper is motivated by the need to improve the post-Newtonian (PN) amplitude accuracy of waveforms for gravitational waves generated by inspiralling compact binaries, both for use in data analysis and in the comparison between post-Newtonian approximations and numerical relativity computations. It presents (i) the non-linear couplings between multipole moments of general post-Newtonian matter sources up to order 3.5PN, including all contributions from tails, tails-of-tails and the non-linear memory effect; and (ii) the source mass-type octupole moment of (non-spinning) compact binaries up to order 3PN, which permits completion of the expressions of the octupole modes and of the gravitational waveform to order 3.5PN. On this occasion we reconfirm by means of independent calculations our earlier results concerning the source mass-type quadrupole moment to order 3PN. Related discussions on factorized resummed waveforms and the occurence of logarithmic contributions to high order are also included.