Cauchy surfaces and diffeomorphism types of globally hyperbolic spacetimes

TL;DR

This paper extends the understanding of globally hyperbolic spacetimes by showing that their diffeomorphism types are determined by the h-cobordism class of their Cauchy surfaces across arbitrary dimensions.

Contribution

It generalizes Chernov-Nemirovski's result from 4-manifolds to higher dimensions, linking the spacetime's diffeomorphism type to the h-cobordism class of Cauchy surfaces.

Findings

Diffeomorphism type determined by h-cobordism class

Extension of previous 4D results to arbitrary dimensions

Connection between spacetime topology and Cauchy surface topology

Abstract

Chernov-Nemirovski observed that the existence of a globally hyperbolic Lorentzian metric on a (3 + 1)-spacetime pins down a smooth structure on the underlying 4-manifold. In this paper, we point out that the diffeomorphism type of a globally hyperbolic (n + 1)-spacetime is determined by the h-cobordism class of its Cauchy surface, hence extending Chernov-Nemirovski's observation to arbitrary dimensions.