Journal
LETTERS IN MATHEMATICAL PHYSICS
Volume 110, Issue 1, Pages 83-103Publisher
SPRINGER
DOI: 10.1007/s11005-019-01213-8
Keywords
Causality theory; Low regularity; Chronological future; Causal bubbles
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Funding
- STFC [ST/L000490/1] Funding Source: UKRI
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We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschitz curves) may be non-open and may differ from the corresponding sets defined via piecewise C1\documentclass[12pt]-curves. By refining the notion of a causal bubble from Chrusciel and Grant (Class Quantum Gravity 29(14):145001, 2012), we characterize spacetimes for which such phenomena can occur, and also relate these to the possibility of deforming causal curves of positive length into timelike curves (push-up). The phenomena described here are, in particular, relevant for recent synthetic approaches to low-regularity Lorentzian geometry where, in the absence of a differentiable structure, causality has to be based on locally Lipschitz curves.
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