Globally hyperbolic spacetimes are defined as Lorentz manifolds without closed nonspacelike curves and naked singularities. They form one of the most important classes of spacetimes.

We show that for a vast class of topological 4-manifolds only one of the possible smooth structures on them is compatible with a globally hyperbolic Lorentz metric.

Newman and Clarke observed that a given smooth 4-manifold could admit many globally hyperbolic Lorentz metrics with pairwise non homeomorphic Cauchy surfaces. For a large class of spacetimes X we show that the Cauchy surface M can be determined from the manifold N_X=ST^*M of all light rays in X. This is related to the question on whether one can tell the smooth structure on M from the contact manifold ST^*M.

Based on a joint work with Stefan Nemirovski