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arXiv · 2002.03949

The contact structure on the space of null geodesics of causally simple spacetimes

Jakob Hedicke
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Abstract

It is shown that the space of null geodesics of a star-shaped causally simple subset of Minkowski space is contactomorphic to the canonical contact structure in the spherical cotangent bundle of $\mathbb{R}^n$. In the $3$-dimensional case we prove a similar result for a large class of causally simple contractible subsets of an arbitrary globally hyperbolic spacetime applying methods from the theory of contact-convex surfaces. Moreover we prove that under certain assumptions the space of null geodesics of a causally simple spacetime embeds with smooth boundary into the space of null geodesics of a globally hyperbolic spacetime. The characteristic foliation of this boundary provides an invariant of the conformal class of the causally simple spacetime.

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Jakob Hedicke. 2020-02-10. The contact structure on the space of null geodesics of causally simple spacetimes. https://arxiv.org/abs/2002.03949

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