Global hyperbolicity meets order completeness

Abstract

Recently, an order completeness property has attracted attention in some low regularity spacetime geometry literature, where it was named `chronocompleteness'. In this work we prove that, in the framework of standard Lorentzian geometry, this property is equivalent to global hyperbolicity. The equivalence of global hyperbolicity with other more traditional forms of order completeness is also established.

arXiv comment14 pages. v3: some simplifications in two proofs. Matches published version