Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 40, Issue 18, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-6382/acdd40
Keywords
low regularity; causality; Lorentzian length spaces
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The definitions of global hyperbolicity for closed cone structures and topological preordered spaces coincide with those in recent literature on Lorentzian length spaces and Lorentzian optimal transport. In Kunzinger-Samann's Lorentzian length spaces, the definition of global hyperbolicity coincides with that for closed cone structures and topological preordered spaces.
The definitions of global hyperbolicity for closed cone structures and topological preordered spaces are known to coincide. In this work we clarify the connection with definitions of global hyperbolicity proposed in recent literature on Lorentzian length spaces and Lorentzian optimal transport, suggesting possible corrections for the terminology adopted in these works. It is found that in Kunzinger-Samann's Lorentzian length spaces the definition of global hyperbolicity coincides with that valid for closed cone structures and, more generally, for topological preordered spaces: the causal relation is a closed order and the causally convex hull operation preserves compactness. In particular, it is independent of the metric, chronological relation or Lorentzian distance.
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