Domain Theory and the Causal Structure of Space-Time

  • Keye Martin
  • Prakash Panangaden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5028)


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.


Causal Structure Domain Theory Timelike Curve Spacetime Structure Manifold Topology 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Keye Martin
    • 1
  • Prakash Panangaden
    • 2
  1. 1.Naval Research LaboratoryCenter for High Assurance Computer SystemsWashingtonUSA
  2. 2.School of Computer ScienceMcGill UniversityMontrealCanada

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