On the completeness of impulsive gravitational wave space-times

Abstract

We consider a class of impulsive gravitational wave space-times, which generalize impulsive pp-waves. They are of the form $M=N\times {\mathbb{R}}_1^2$, where $(N,h)$ is a Riemannian manifold of arbitrary dimension and $M$ carries the line element $d{s}^2=d{h}^2+2dudv+f(x)\delta (u)d{u}^2$ with $d{h}^2$ the line element of $N$ and $\delta$ the Dirac measure. We prove a completeness result for such space-times $M$ with complete Riemannian part $N$.

13 pages, minor changes suggested by the referees

References in corpus (1)

• The use of Generalised Functions and Distributions in General Relativity