Continuous representation of a globally hyperbolic spacetime with non-compact Cauchy surfaces

Abstract

In this paper we consider a Lorentzian manifold which is globally hyperbolic with a non-compact Cauchy surface. We show that continuous representation of the spacetime is possible by causally admissible systems of its Cauchy surfaces. For that purpose we use Vietoris topology. One application is also included. The work is in the line with research on causality in relativistic spacetimes.