# Radiation Memory, Boosted Schwarzschild Spacetimes and Supertranslations

## TL;DR

This paper explores gravitational memory effects and supertranslations in boosted Schwarzschild spacetimes, providing a new framework for understanding nonlinear gravitational wave memory and its impact on asymptotic symmetries.

## Contribution

It introduces a novel approach using Kerr-Schild metrics to analyze nonlinear gravitational memory effects in boosted Schwarzschild spacetimes.

## Key findings

- Proper retarded solutions are described by ingoing Kerr-Schild metrics.
- Nonlinear memory effects are linked to supertranslations and angular momentum conservation.
- The Kerr-Schild approach extends to nonlinear regimes, offering new insights.

## Abstract

We investigate gravitational radiation memory and its corresponding effect on the asymptotic symmetries of a body whose exterior is a boosted Schwarzschild spacetime. First, in the context of linearized theory, we consider such a Schwarzschild body which is initially at rest, then goes through a radiative stage and finally emerges as a boosted Schwarzschild body. We show that the proper retarded solution of the exterior Schwarzschild spacetime for this process can be described in terms of the ingoing Kerr-Schild form of the Schwarzschild metric for both the initial and final states. An outgoing Kerr-Schild or time symmetric metric does not give the proper solution. The special property of Kerr-Schild metrics that their linearized and nonlinear forms are identical allows us to extend this result to processes in the nonlinear regime. We then discuss how the nonlinear memory effect, and its associated supertranslation, affect angular momentum conservation. Our approach provides a new framework for studying nonlinear aspects of the memory effect.