A domain of spacetime intervals in general relativity
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.
Causality
spacetime
global hyperbolicity
interval domains
bicontinuous posets
spacetime topology
1-28
Regular Paper
Keye
Martin
Keye Martin
Prakash
Panangaden
Prakash Panangaden
10.4230/DagSemProc.04351.5
Creative Commons Attribution 4.0 International license
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