Nonlinear Gravitational Memory in the Post-Minkowskian Expansion

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 ( G 3 ) multipolar waveform, thus providing a useful benchmark for future calculations of this quantity.