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arXiv · 2610.20451

Analytical Time-Domain Waveforms for Black-Hole Scattering in the Self-Force Expansion

Chris Kavanagh·Julio Parra-Martinez·Davide Usseglio
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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 $F_D^{(3)}$, 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.

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Chris Kavanagh, Julio Parra-Martinez, Davide Usseglio. 2026-10-14. Analytical Time-Domain Waveforms for Black-Hole Scattering in the Self-Force Expansion. https://arxiv.org/abs/2610.20451

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