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It is shown that the space of null geodesics of a star-shaped causally simplesubset of Minkowski space is contactomorphic to the canonical contact structurein the spherical cotangent bundle of $\mathbb{R}^n$. In the $3$-dimensionalcase we prove a similar result for a large class of causally simplecontractible subsets of an arbitrary globally hyperbolic spacetime applyingmethods from the theory of contact-convex surfaces. Moreover we prove thatunder certain assumptions the space of null geodesics of a causally simplespacetime embeds with smooth boundary into the space of null geodesics of aglobally hyperbolic spacetime. The characteristic foliation of this boundaryprovides an invariant of the conformal class of the causally simple spacetime.

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