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.
Categories: math.DG math-ph math.MP math.SG