# Scaling and conformal symmetries for plane gravitational waves

## TL;DR

This paper explores the symmetries of plane gravitational waves, revealing how isometries and conformal transformations generate conserved quantities and extend our understanding of symmetries in relativistic and non-relativistic frameworks.

## Contribution

It identifies and analyzes the conformal and homothety symmetries of plane gravitational waves, extending previous work on chrono-projective transformations and their role in conserved quantities.

## Key findings

- Isometries are symmetries for both massive and massless particles.
- Conformal extensions are chrono-projective transformations for massless particles.
- Homotheties are universal symmetries for any wave profile.

## Abstract

The isometries of an exact plane gravitational wave are symmetries for both massive and massless particles. Their conformal extensions are in fact chrono-projective transformations introduced earlier by Duval et al are symmetries for massless particles. Homotheties are universal chrono-projective symmetries for any profile. Chrono-projective transformations also generate new conserved quantities for the underlying non-relativistic systems in the Bargmann framework. Homotheties play a similar role for the lightlike "vertical" coordinate as isometries play for the transverse coordinates.