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arXiv · 2506.20733

Nonlinear Gravitational Memory in the Post-Minkowskian Expansion

Alessandro Georgoudis·Vasco Goncalves·Carlo Heissenberg·Julio Parra-Martinez
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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-amplitudes-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 non-analytic-in-frequency part of the $\mathcal{O}(G^3)$ multipolar waveform, thus providing a useful benchmark for future calculations of this quantity.

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Alessandro Georgoudis, Vasco Goncalves, Carlo Heissenberg, Julio Parra-Martinez. 2025-06-25. Nonlinear Gravitational Memory in the Post-Minkowskian Expansion. https://arxiv.org/abs/2506.20733

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