The future is not always open

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 C 1 -curves. By refining the...

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Bibliographic Details
Published in:Letters in mathematical physics 2020-01, Vol.110 (1), p.83-103
Main Authors: Grant, James D. E., Kunzinger, Michael, Sämann, Clemens, Steinbauer, Roland
Format: Article
Language:English
Subjects:
Causality
Complex Systems
Deformation mechanisms
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum gravity
Regularity
Theoretical
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Summary: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 C 1 -curves. By refining the notion of a causal bubble from Chruściel 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.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-019-01213-8