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arXiv · 1901.07996

The future is not always open

James D. E. Grant·Michael Kunzinger·Clemens Sämann·Roland Steinbauer
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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 $C^1$-curves. By refining the notion of a causal bubble from [CG:12],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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James D. E. Grant, Michael Kunzinger, Clemens Sämann, Roland Steinbauer. 2019-09-09. The future is not always open. https://doi.org/10.1007/s11005-019-01213-8

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