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arXiv · 1704.00353

Timelike completeness as an obstruction to $C^0$-extensions

Gregory J. Galloway·Eric Ling·Jan Sbierski
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Abstract

The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike complete and globally hyperbolic Lorentzian manifold is $C^0$-inextendible. For the proof we make use of the result, recently established by S\"amann [17], that even for \emph{continuous} Lorentzian manifolds that are globally hyperbolic, there exists a length-maximizing causal curve between any two causally related points.

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Gregory J. Galloway, Eric Ling, Jan Sbierski. 2017-04-02. Timelike completeness as an obstruction to $C^0$-extensions. https://doi.org/10.1007/s00220-017-3019-2

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