Existence of instantaneous Cauchy surfaces

Abstract

Several properties of instantaneous Cauchy surfaces are obtained. It is shown that a strongly causal spacetime admits an instantaneous Cauchy surface through each of its points, that there is a close and reversible relationship between these surfaces and maximal open globally hyperbolic subsets, that every instantaneous Cauchy surface is contained in a maximal instantaneous Cauchy surface, and that the latter surface is a maximal achronal surface which separates spacetime into past, present, and future. Some other properties of instantaneous Cauchy surfaces are discussed along with a refinement of an earlier topology change property.