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 (5)

• The use of Generalised Functions and Distributions in General Relativity
• A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves
• Geodesics and geodesic deviation for impulsive gravitational waves
• On General Plane Fronted Waves. Geodesics
• Geodesics for impulsive gravitational waves and the multiplication of distributions

Cited by in corpus (9)

• Global hyperbolicity for spacetimes with continuous metrics
• Gyratonic pp-waves and their impulsive limit
• The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, Part I
• The memory effect in impulsive plane waves: comments, corrections, clarifications
• Completeness of general pp-wave spacetimes and their impulsive limit
• Ehlers-Kundt Conjecture about Gravitational Waves and Dynamical Systems
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, II
• The globally hyperbolic metric splitting for non-smooth wave-type space-times