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

Abstract : 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 $(3,3)$ ( 3 , 3 ) and $(3,1)$ ( 3 , 1 ) 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.
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Journal articles

https://hal-insu.archives-ouvertes.fr/insu-03644768
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Submitted on : Tuesday, April 19, 2022 - 2:03:21 PM
Last modification on : Wednesday, April 20, 2022 - 3:40:08 AM

### Citation

Guillaume Faye, Luc Blanchet, Bala R. Iyer. Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order. Classical and Quantum Gravity, 2015, 32, ⟨10.1088/0264-9381/32/4/045016⟩. ⟨insu-03644768⟩

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