Analytical Time-Domain Waveforms for Black-Hole Scattering in the Self-Force Expansion
Abstract
We obtain a systematic understanding of the time-domain gravitational waveform of hyperbolic black-hole scattering at first order in the self-force expansion and all orders in the post-Newtonian/post-Minkowskian (PN/PM) expansion. The continuous frequency spectrum of unbound orbits makes the inverse Fourier transform to the time domain diverge order by order; we introduce a dimensional-regularization-inspired prescription that cures this uniformly. We show that the full waveform then follows, at any PM and PN order, from a single family of integrals, generated by the Lauricella function FD(3), which we calculate using strategies familiar from the study of Feynman integrals. As a proof of principle, we use this understanding to compute the quadrupolar 1SF waveform through relative 10PM-20PN, that is to order cal O(G10 v42), the full 1SF waveform to 10PM-10PN, as well as the asymptotic fluxes and the dissipative scattering angle at the corresponding accuracy.
Related
- Analytical Time-Domain Waveforms for Black-Hole Scattering in the Post-Minkowskian Expansion
- Binary black hole scattering in the extreme-mass-ratio limit: time-domain waveform
- On the Time-Domain Waveforms Leading to Frequency Comb Spectra
- A Transformer model for precessing binary black-hole merger waveforms calibrated to numerical relativity
- Surrogate model of gravitational waveforms for quasi-circular, spin-aligned, asymmetric-mass black hole binaries based on the hybridization of WaSABI-C inspirals with numerical relativity waveforms
BibTeX
@misc{kavanagh2026analytical,
title = {{Analytical Time-Domain Waveforms for Black-Hole Scattering in the Self-Force Expansion}},
author = {Chris Kavanagh and Julio Parra-Martinez and Davide Usseglio},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20451},
eprint = {2610.20451},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05843924v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analytical Time-Domain Waveforms for Black-Hole Scattering in the Self-Force Expansion
AU - Chris Kavanagh
AU - Julio Parra-Martinez
AU - Davide Usseglio
PY - 2026
DA - 2026/10/22
PB - HAL
DO - 10.48550/arxiv.2610.20451
UR - https://hal.science/hal-05843924v1
AB - We obtain a systematic understanding of the time-domain gravitational waveform of hyperbolic black-hole scattering at first order in the self-force expansion and all orders in the post-Newtonian/post-Minkowskian (PN/PM) expansion. The continuous frequency spectrum of unbound orbits makes the inverse Fourier transform to the time domain diverge order by order; we introduce a dimensional-regularization-inspired prescription that cures this uniformly. We show that the full waveform then follows, at any PM and PN order, from a single family of integrals, generated by the Lauricella function F_D^(3), which we calculate using strategies familiar from the study of Feynman integrals. As a proof of principle, we use this understanding to compute the quadrupolar 1SF waveform through relative 10PM-20PN, that is to order cal O(G^10 v^42), the full 1SF waveform to 10PM-10PN, as well as the asymptotic fluxes and the dissipative scattering angle at the corresponding accuracy.
ER -