Study of topological and physical properties of Schwarzschild space and Kerr space equipped with Zeeman Topology

Abstract

The Zeeman topology, first proposed by E. C. Zeeman in 1967, is a topology for Minkowski space that is physically well-motivated, but more intricate than the standard Euclidean topology. Later, it was extended to general relativity in 1976 by R. Göbel. Despite its compatibility with pseudo-Riemannian geometry, the Zeeman topology is rarely used in the literature due to its lack of second-countability. This work aims to explore the implications of the Zeeman topology for Schwarzschild and Kerr space-time. Specifically, we investigate the compactness of trapped surfaces and the validity of the singularitytheorem. Our findings suggest that the Zeeman topology may offer alternative views to certain physical phenomena in general relativity.