Stable singularities of wave-fronts in general relativity

Abstract

A wave-front in a space-time $\mathcal{M}$ is a family of null geodesics orthogonal to a smooth spacelike two-surface in $\mathcal{M}$; it is of some interest to know how a wave-front can fail to be a smoothly immersed surface in $\mathcal{M}$. In this paper we see that the space of null geodesics $\mathcal{N}$ of $\mathcal{M}$, 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.

5 pages

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