# The Memory Effect for Plane Gravitational Waves

## TL;DR

This paper explores the gravitational memory effect in exact plane wave solutions, showing how soft gravitons influence particle motion and proposing velocity memory as a detection method for gravitational waves.

## Contribution

It provides an exact analysis of the gravitational memory effect in plane wave spacetimes, including a new proof of Bondi and Pirani's caustic theorem and insights into velocity memory detection.

## Key findings

- Asymptotic relative velocity remains constant but non-zero.
- The velocity memory effect can be used to detect gravitational waves.
- Contradicts previous claims of permanent displacement by Zel'dovich and Polnarev.

## Abstract

We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einstein's vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel'dovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the "velocity memory effect", considered by Braginsky, Thorne, Grishchuk, and Polnarev.