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

2020/02/10 by Hedicke, Jakob · 2 citations
#53C22 #53C50 #53C80 #53D10 #57R17 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2002.03949

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 ℝⁿ. 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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• On the space of cone geodesics and positive paths of contactomorphisms
• Finslerian lightconvex boundaries: applications to causal simplicity and the space of cone geodesics N

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