Non-expanding impulsive gravitational waves

TL;DR

This paper studies impulsive gravitational waves in Minkowski and (anti-)de Sitter spaces, showing their classification and properties, including equivalence of certain subclasses and explicit continuous coordinate systems.

Contribution

It classifies impulsive gravitational waves within the Kundt class $P( extstyleackslashLambda)$ and demonstrates their equivalence and explicit coordinate representations.

Findings

Impulsive pp-waves are the only non-trivial impulsive waves in Minkowski space.

Subclasses of $P( extstyleackslashLambda)$ are locally equivalent for impulsive profiles when $ extstyleackslashLambda eq 0$.

A continuous coordinate system for these impulsive solutions is provided.

Abstract

We investigate a class of impulsive gravitational waves which propagate either in Minkowski or in the (anti-)de Sitter background. These waves are constructed as impulsive members of the Kundt class $P(\Lambda)$ of non-twisting, non-expanding type N solutions of vacuum Einstein equations with a cosmological constant $\Lambda$. We show that the only non-trivial waves of this type in Minkowski spacetime are impulsive pp-waves. For $\Lambda\not=0$ we demonstrate that the canonical subclasses of $P(\Lambda)$, which are invariantly different for smooth profiles, are all locally equivalent for impulsive profiles. Also, we present coordinate system for these impulsive solutions which is explicitly continuous.