Some topological results on a globally hyperbolic spacetime
with non-compact Cauchy surfaces
Masoud Bahrami Seif Abad\,^1 and Mehdi Sharifzadeh\,^2
\,^{1,2}Department of Mathematics, Yasouj University,Daneshjo Ave. 75918-74831 Yasouj, Iran
Pages 388–394 | Received 24 July 2024, Accepted 26 August 2024, Published 08 November 2024
Abstract
This paper studies new topologies on globally hyperbolic spacetimes with non-compact Cauchy surfaces, demonstrating that these topologies are T1 but not Hausdorff, and are contained within manifold topology. The authors have derived certain properties of these topologies and shown that a continuous representation of a globally hyperbolic spacetime with a non-compact Cauchy surface is possible, based on the causally admissible systems of its Cauchy surface.
Keywords: Spacetime, Globally Hyperbolic, Order Isomorphism, Vietoris Topology, Causally Admissible System.
MSC numbers: 06B35, 53C50, 83C99.
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