# Soft Gravitons & the Memory Effect for Plane Gravitational Waves

## TL;DR

This paper explores the gravitational memory effect caused by plane gravitational waves, linking it to soft gravitons, and discusses detection methods, solutions, extensions to Einstein-Maxwell waves, and a quantization approach.

## Contribution

It provides a detailed analysis of the memory effect for plane waves, connecting it to soft gravitons and extending the framework to Einstein-Maxwell solutions with quantization.

## Key findings

- Numerical confirmation of the relevance of Riemann tensor integrals
- Construction of solutions for various wave profiles
- Extension to Einstein-Maxwell plane waves and quantization

## Abstract

The "gravitational memory effect" due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with soft gravitons. It is explained how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midi-superspace quantization is given.