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Stable singularities of wave-fronts in general relativity

Robert J Low
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Abstract

A wave-front in a space-time $\cal M$ is a family of null geodesics orthogonal to a smooth spacelike two-surface in $\cal M$; it is of some interest to know how a wave-front can fail to be a smoothly immersed surface in $\cal M$. In this paper we see that the space of null geodesics $\cal N$ of $\cal M$, considered as a contact manifold, provides a natural setting for an efficient study of the stable singularities arising in the time evolution of wave-fronts.

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Robert J Low. 2001-08-03. Stable singularities of wave-fronts in general relativity. https://doi.org/10.1063/1.532257

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