Generalized Symmetries of Impulsive Gravitational Waves

TL;DR

This paper extends the classification of symmetries in impulsive gravitational waves by including non-smooth transformations, revealing a richer symmetry algebra structure.

Contribution

It introduces a generalized framework for symmetries of impulsive gravitational waves, allowing non-smooth transformations and expanding the symmetry algebra.

Findings

Extended the symmetry group to include non-smooth diffeomorphisms.

Discovered a richer structure of the symmetry algebra.

Generalized previous classifications to impulsive profiles.

Abstract

We generalize previous \cite{AiBa2} work on the classification of ($C^\infty$) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normal-form-preserving diffeomorphisms to include non-smooth transformations. This extension entails a richer structure of the symmetry algebra generated by the (non-smooth) Killing vectors.