Spacetimes as Topological Spaces, and the Need to Take Methods of General Topology More Seriously

Kyriakos Papadopoulos () and Fabio Scardigli ()
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Kyriakos Papadopoulos: Kuwait University, Department of Mathematics
Fabio Scardigli: Politecnico di Milano, Dipartimento di Matematica

Chapter Chapter 6 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 185-196 from Springer

Abstract: Abstract Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime: a topology sufficient for the description of spacetime singularities or a topology which incorporates the causal structure? Or both? Is it more preferable to consider a topology with as many physical properties as possible, whose description might be complicated and counterintuitive, or a topology which can be described via a countable basis but misses some important information? These are just a few from the questions that we ask in this chapter, which serves as a critical review of the terrain and contains a survey with remarks, corrections and open questions.

Keywords: Zeeman-Göbel topologies; Topologising a spacetime; Spacetime singularities; Causal topologies; Manifold topology (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/978-3-030-15242-0_6

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