License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.04351.5
URN: urn:nbn:de:0030-drops-1350
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2005/135/
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Martin, Keye ; Panangaden, Prakash

A domain of spacetime intervals in general relativity

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04351.PanangadenPrakash.Paper.135.pdf (0.2 MB)

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:DagSemProc.04351.5,
  author =	{Martin, Keye and Panangaden, Prakash},
  title =	{{A domain of spacetime intervals in general relativity}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--28},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2005/135},
  URN =		{urn:nbn:de:0030-drops-1350},
  doi =		{10.4230/DagSemProc.04351.5},
  annote =	{Keywords: Causality , spacetime , global hyperbolicity , interval domains , bicontinuous posets , spacetime topology}
}

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

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