Memories of Gravitational Shockwaves

TL;DR

This paper investigates how gravitational shockwaves influence classical fields and the resulting memory effects, revealing that fields retain only the shock's spatial profile, which can be described through geometric transformations.

Contribution

It demonstrates that gravitational memory effects depend solely on the spatial profile of shockwaves and introduces a geometric framework using supertranslations to describe field transformations.

Findings

Fields remember only the spatial profile of the shock.

Memory effects can be expressed as supertranslation transformations.

Results have potential applications in astrophysics.

Abstract

Gravitational shockwaves produce perturbations of field systems. We study classical scalar and electromagnetic fields and gravitational memory effects left after the action on the fields of plane-fronted gravitational shockwaves. The gravitational memory plays a key role for the choice of Cauchy data which determine the perturbations. We demonstrate that field systems`remember' only a spatial `profile' of the shock, but not the form of the signal. Moreover the dependence on the spatial profile can be expressed in a geometric way as a transformation of fields under coordinate supertranslations defined near the shockwave front. We also discuss applications of our results to astrophysics.