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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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Abstract

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 :
NameEmailORCID
Grant, James D. E.j.grant@surrey.ac.uk
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 (http://creativecommons.org/licenses/by/4.0/), 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
URI: http://epubs.surrey.ac.uk/id/eprint/852818

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