On smooth Cauchy hypersurfaces and Geroch's splitting theorem

Abstract

Given a globally hyperbolic spacetime $M$, we show the existence of a {\em smooth spacelike} Cauchy hypersurface $S$ and, thus, a global diffeomorphism between $M$ and $\mathbb{R}\times S$.

Minor tipographical corrections; 12 pages, Latex; to appear in Commun. Math. Phys

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