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 Sämann (Ann Henri Poincaré 17(6):1429–1455, 2016), that even for continuous Lorentzian manifolds that are globally hyperbolic, there exists a length-maximizing causal curve between any two causally related points.
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Communicated by P.T. Chrusciel
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Galloway, G.J., Ling, E. & Sbierski, J. Timelike Completeness as an Obstruction to C 0-Extensions. Commun. Math. Phys. 359, 937–949 (2018). https://doi.org/10.1007/s00220-017-3019-2
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DOI: https://doi.org/10.1007/s00220-017-3019-2