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Radiated energy spectrum, radiated angular distribution and nonlinear memory from the one-loop gravitational bremsstrahlung waveform

Donato Bini1, Thibault Damour2, Stefano De Angelis3, and Andrea Geralico1

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Phys. Rev. D 114, 084088 – Published 30 October, 2026

DOI: https://doi.org/10.1103/kl8k-4f3b

Abstract

The frequency-domain gravitational waveform emitted by the scattering of two nonspinning massive particles has recently been derived at next-to-leading, i.e., one-loop, post-Minkowskian order, h(ω,θ,ϕ)∼G2+G3. Building on this one-loop-accurate frequency-domain gravitational waveform, we successively derive the spectral gravitational-wave (GW) radiance, dEgw/(dωdΩ), the radiated GW energy spectrum, dEgw/dω, and the radiated GW angular distribution, dEgw/dΩ, up to order G4 included. We deduce from the radiated angular distribution the multipole expansion of the nonlinear memory up to order G5 included, thereby extending previous results. We work in the center-of-mass frame, and our results reach the fractional 7.5PN accuracy. For completeness, we include the tree-level information (considered in the center-of-mass frame).

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References (39)

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Phys. Rev. D 114, 084088– Published 30 October, 2026
  • Received 4 July 2026
  • Accepted 17 September 2026
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