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The future is not always open

Grant, James D. E., Kunzinger, Michael, Sämann, Clemens and Steinbauer, Roland (2019) The future is not always open Letters in Mathematical Physics.

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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 -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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Grant, James D.
Kunzinger, Michael
Sämann, Clemens
Steinbauer, Roland
Date : 2019
DOI : 10.1007/s11005-019-01213-8
Copyright Disclaimer : © The Author(s) 2019. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Uncontrolled Keywords : Causality theory; Low regularity; Chronological future; Causal bubbles
Depositing User : Clive Harris
Date Deposited : 26 Sep 2019 15:58
Last Modified : 26 Sep 2019 15:58

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