DagSemProc.04351.5.pdf
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A domain of spacetime intervals in general relativity
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Dagstuhl Seminar Proceedings, Volume 4351
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2005-04-22
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Keye Martin and Prakash Panangaden. A domain of spacetime intervals in general relativity. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)
https://doi.org/10.4230/DagSemProc.04351.5
https://doi.org/10.4230/DagSemProc.04351.5
Abstract
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This implies 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 emanates from
something discrete.
Keywords
- Causality
- spacetime
- global hyperbolicity
- interval domains
- bicontinuous posets
- spacetime topology
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