TY - JOUR

T1 - Timelike Completeness as an Obstruction to C 0-Extensions

AU - Galloway, Gregory J.

AU - Ling, Eric

AU - Sbierski, Jan

N1 - Funding Information:
Acknowledgements. Jan Sbierski would like to thank Magdalene College, Cambridge, for their financial support and the University of Miami for hospitality during a visit when this project was started. The authors are grateful to Piotr Chrus´ciel, Ettore Minguzzi, and the anonymous referees for some helpful comments. The authors also thank Clemens Sämann for bringing to their attention the paper [17].

PY - 2018/5/1

Y1 - 2018/5/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-017-3019-2

DO - 10.1007/s00220-017-3019-2

M3 - Article

AN - SCOPUS:85033459992

VL - 359

SP - 937

EP - 949

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -