On the completeness of impulsive gravitational wave spacetimes

Abstract

We consider a class of impulsive gravitational wave spacetimes, which generalize impulsive pp-waves. They are of the form , where (N, h) is a Riemannian manifold of arbitrary dimension and M carries the line element ds2 = dh2 + 2 du dv + f(x)δ(u) du2, with dh2 being the line element of N and δ the Dirac measure. We prove a completeness result for such spacetimes M with complete Riemannian part N.