Gravitational Waves: Just Plane Symmetry

TL;DR

This paper explores the unique symmetry properties of gravitational plane wave spacetimes, revealing that they satisfy all covariant vacuum field equations except Einstein's, and discusses their mini-superspace models.

Contribution

It uncovers the special symmetry group properties of gravitational plane waves and their implications for vacuum solutions in general relativity.

Findings

Metrics with plane wave symmetry satisfy all covariant vacuum equations except Einstein's.

The proof utilizes homothety and scaling behaviors of the field equations.

Discusses a mini-superspace description of such spacetimes.

Abstract

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also discuss a mini-superspace description of spacetimes with plane wave symmetry.