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A domain of spacetime intervals in general relativity

Authors Keye Martin, Prakash Panangaden

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DagSemProc.04351.5.pdf
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Keywords
  • Causality
  • spacetime
  • global hyperbolicity
  • interval domains
  • bicontinuous posets
  • spacetime topology

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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.

Cite As Get BibTex

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

Author Details

Keye Martin
Prakash Panangaden
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