A domain of spacetime intervals in general relativity

TL;DR

This paper demonstrates that a globally hyperbolic spacetime in general relativity can be reconstructed purely from order-theoretic data, specifically a dense set of events and causality relations, by linking it to interval domains.

Contribution

It introduces a novel order-theoretic method to reconstruct globally hyperbolic spacetimes from minimal data, connecting spacetime geometry with domain theory.

Findings

Reconstruction of spacetime from a countable dense set and causality.

Equivalence between globally hyperbolic spacetimes and interval domains.

Purely order-theoretic approach to spacetime geometry.

Abstract

Beginning 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.