Cauchy surfaces and diffeomorphism types of globally hyperbolic spacetimes

Chernov-Nemirovski observed that the existence of a globally hyperbolic Lorentzian metric on a $(3+1)$ ( 3 + 1 ) -spacetime pins down a smooth structure on the underlying four-manifold. In this paper, we point out that the diffeomorphism type of a globally hyperbolic $(n+1)$ ( n + 1 ) -spacetime is determined by the h-cobordism class of its Cauchy surface, hence extending Chernov-Nemirovskiʼs observation to arbitrary dimensions.