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Nonlinear Gravitational Memory in the Post-Minkowskian Expansion

Alessandro Georgoudis1, Vasco Goncalves2, Carlo Heissenberg3, and Julio Parra-Martinez4

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Phys. Rev. Lett. 136, 121401 – Published 24 March, 2026

DOI: https://doi.org/10.1103/8m17-s2y8

Abstract

We present the first computation of the nonlinear gravitational memory waveform for the scattering of two compact objects in general relativity at leading order in the post-Minkowskian expansion. We use the scattering-amplitude-based representation of the gravitational waveform, which naturally expresses the nonlinear memory as the contribution of soft gravitons emitted by the gravitational waves themselves. We perform the calculation by applying a multipolar decomposition to the waveform and using the reverse unitarity method to obtain explicit exact-in-velocity predictions. We validate the results by calculating the corresponding velocity-expanded post-Newtonian multipoles, finding perfect agreement. Our results complete the knowledge of the gauge-invariant nonanalytic-in-frequency part of the O(G3) multipolar waveform, thus providing a useful benchmark for future calculations of this quantity.

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Phys. Rev. Lett. 136, 121401– Published 24 March, 2026
  • Received 12 September 2025
  • Revised 26 November 2025
  • Accepted 19 February 2026
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