Octupolar bremsstrahlung waveform up to the two-loop level and the third-and-a-half post-Newtonian accuracy
Abstract
Extending our recent work (which focussed on the even-parity quadrupolar part of the waveform), we compute the even-parity octupolar contribution, U3, to the gravitational waveform W ≡ (c4 r)/4G m̅i m̅j hi j emitted during the scattering of two masses. We work within the Multipolar Post-Minkowskian (MPM) formalism, and use the 3.5 Post-Newtonian (PN) accurate radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We explicitly evaluate the frequency-domain value Û3(ω, θ,ϕ) of U3 up to the 2-loop level, i.e. $ O(G^4)$ contributions to hij(ω, θ,ϕ), corresponding to O(G3) contributions to Û3(ω, θ,ϕ). As a crucial partial confirmation of our result, we find that the 1-loop truncation of our 3.5 PN frequency-domain MPM waveform agrees with corresponding existing Effective Field Theory (EFT) results when taking into account exactly the {\it same} (2.5PN-level) difference in the definitions of the center-of-mass origins within the two formalisms that was deduced from our previous quadrupolar comparison.
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BibTeX
@misc{bini2026octupolar,
title = {{Octupolar bremsstrahlung waveform up to the two-loop level and the third-and-a-half post-Newtonian accuracy}},
author = {Donato Bini and Thibault Damour and Andrea Geralico},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11835},
eprint = {2609.11835},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05761200v1},
}
RIS
TY - UNPB
TI - Octupolar bremsstrahlung waveform up to the two-loop level and the third-and-a-half post-Newtonian accuracy
AU - Donato Bini
AU - Thibault Damour
AU - Andrea Geralico
PY - 2026
DA - 2026/09/10
PB - HAL
DO - 10.48550/arxiv.2609.11835
UR - https://hal.science/hal-05761200v1
AB - Extending our recent work (which focussed on the even-parity quadrupolar part of the waveform), we compute the even-parity octupolar contribution, U_3, to the gravitational waveform W ≡ (c^4 r)/4G m̅^i m̅^j h_i j emitted during the scattering of two masses. We work within the Multipolar Post-Minkowskian (MPM) formalism, and use the 3.5 Post-Newtonian (PN) accurate radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We explicitly evaluate the frequency-domain value Û_3(ω, θ,ϕ) of U_3 up to the 2-loop level, i.e. $ O(G^4)$ contributions to h_ij(ω, θ,ϕ), corresponding to O(G^3) contributions to Û_3(ω, θ,ϕ). As a crucial partial confirmation of our result, we find that the 1-loop truncation of our 3.5 PN frequency-domain MPM waveform agrees with corresponding existing Effective Field Theory (EFT) results when taking into account exactly the {\it same} (2.5PN-level) difference in the definitions of the center-of-mass origins within the two formalisms that was deduced from our previous quadrupolar comparison.
ER -