Nonlinear Gravitational Memory in the Post-Minkowskian Expansion

TL;DR

This paper computes the first nonlinear gravitational memory waveform for scattering of two compact objects in General Relativity using a post-Minkowskian expansion, employing scattering amplitudes and validating with post-Newtonian results.

Contribution

It introduces a novel calculation of the nonlinear gravitational memory waveform at leading order in the post-Minkowskian expansion using amplitude methods.

Findings

Explicit exact-in-velocity predictions for the waveform.

Validation of results with post-Newtonian multipoles.

Completes the gauge-invariant non-analytic-in-frequency waveform at (G^3).

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.