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arXiv · 1207.2633

On the completeness of impulsive gravitational wave space-times

Clemens Sämann·Roland Steinbauer
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Abstract

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

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Clemens Sämann, Roland Steinbauer. 2012-11-19. On the completeness of impulsive gravitational wave space-times. https://doi.org/10.1088/0264-9381%2F29%2F24%2F245011

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