Timelike Completeness as an Obstruction to C 0-Extensions

Gregory J. Galloway, Eric Ling, Jan Sbierski

Research output: Contribution to journalArticle

11 Scopus citations

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 C0-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.

Original languageEnglish (US)
Pages (from-to)937-949
Number of pages13
JournalCommunications in Mathematical Physics
Volume359
Issue number3
DOIs
StatePublished - May 1 2018

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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