Globally hyperbolic spacetime

Summary

A globally hyperbolic spacetime is a causal, time-oriented Lorentzian manifold. In it, the set of events lying between any two events is compact. It is the strongest of the usual causality conditions. Globally hyperbolic spacetimes are exactly those with a Cauchy surface, a moment of time from which the whole past and future are determined. They are the natural setting for the initial value problem of general relativity and for wave equations on curved spacetimes.