Memory and supertranslations on plane wave spacetimes: an on-shell perspective

TL;DR

This paper derives a comprehensive tree-level gravitational waveform in plane wave spacetimes using on-shell amplitude methods, revealing how memory effects relate to boundary conditions and supertranslations.

Contribution

It provides the first explicit tree-level waveform expression capturing all memory effects in plane wave backgrounds, linking boundary conditions, supertranslations, and waveform phase shifts.

Findings

Derived the first explicit waveform with all memory effects.

Connected boundary conditions to gravitational memory and supertranslations.

Showed supertranslations induce waveform phase shifts in plane wave backgrounds.

Abstract

We revisit the computation of the classical gravitational waveform for a particle moving in a plane wave background using on-shell amplitudes. We emphasize the relationship between gravitational memory and the boundary conditions of external scattering states, which were neglected in previous works. We then provide the first tree-level expression for the waveform that captures all memory effects. The waveform is presented in terms of Synge's world function, with explicit tail terms, and a smooth weak memory limit. We also discuss the choice of BMS frame for the waveform on a plane wave background. In flat space, this corresponds to a choice of soft dressing of the initial state. We show that on a plane wave background, this dressing becomes a supertranslation of the waveform, in addition to a phase shift in the waveshape of the background.