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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="script">O</a:mi> <a:mo stretchy="false">(</a:mo> <a:msup> <a:mi>G</a:mi> <a:mn>3</a:mn> </a:msup> <a:mo stretchy="false">)</a:mo> </a:math> multipolar waveform, thus providing a useful benchmark for future calculations of this quantity.