Expanding impulsive gravitational waves

TL;DR

This paper shows that expanding impulsive spherical gravitational waves can be derived as limits of Robinson-Trautman solutions across various backgrounds, and extends these to include non-zero cosmological constants with continuous metrics.

Contribution

It demonstrates the impulsive limits of Robinson-Trautman solutions for all subclasses in different backgrounds and introduces a continuous metric formulation, extending to non-zero cosmological constants.

Findings

Impulsive limits of Robinson-Trautman solutions are explicitly demonstrated.

Solutions are expressed in terms of continuous metrics.

Extended to include non-zero cosmological constants.

Abstract

We explicitly demonstrate that the known solutions for expanding impulsive spherical gravitational waves that have been obtained by a "cut and paste" method may be considered to be impulsive limits of the Robinson-Trautman vacuum type N solutions. We extend these results to all the generically distinct subclasses of these solutions in Minkowski, de Sitter and anti-de Sitter backgrounds. For these we express the solutions in terms of a continuous metric. Finally, we also extend the class of spherical shock gravitational waves to include a non-zero cosmological constant.