Timelike completeness as an obstruction to C0-extensions

Gregory J. Galloway, Erick Ling, Jan Sbierski

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 C0-inextendible. For the proof we make use of the result, recently established by Sämann [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.
Original languageEnglish
Pages (from-to)937-949
Number of pages937
JournalCommunications in Mathematical Physics
Issue number3
Early online date5 Nov 2017
Publication statusPublished - 31 May 2018


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