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URN: urn:nbn:de:0030-drops-1350
URL: http://drops.dagstuhl.de/opus/volltexte/2005/135/
Martin, Keye ; Panangaden, Prakash

A domain of spacetime intervals in general relativity

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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.

BibTeX - Entry

@InProceedings{martin_et_al:DSP:2005:135,
  author =	{Keye Martin and Prakash Panangaden},
  title =	{A domain of spacetime intervals in general relativity},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  year =	{2005},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  number =	{04351},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2005/135},
  annote =	{Keywords: Causality , spacetime , global hyperbolicity , interval domains , bicontinuous posets , spacetime topology}
}

Keywords: Causality , spacetime , global hyperbolicity , interval domains , bicontinuous posets , spacetime topology
Seminar: 04351 - Spatial Representation: Discrete vs. Continuous Computational Models
Issue date: 2005
Date of publication: 22.04.2005

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