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A Domain of Spacetime Intervals in General Relativity
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Journal Article
A Domain of Spacetime Intervals in General Relativity
2006
Overview
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emerges from something discrete.
Publisher
Springer,Springer Nature B.V
Subject
/ Domains
/ Exact sciences and technology
/ General relativity and gravitation
/ Global analysis, analysis on manifolds
/ Physics
/ Sciences and techniques of general use
/ Spacetime topology, causal structure, spinor structure
/ Topology
/ Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
