Timelike Completeness as an Obstruction to C<sup>0</sup>-Extensions

Author: 

Galloway, G
Ling, E
Sbierski, J

Publication Date: 

5 November 2017

Journal: 

Communications in Mathematical Physics

Last Updated: 

2021-04-07T01:39:18.68+01:00

DOI: 

10.1007/s00220-017-3019-2

page: 

1-13

abstract: 

© 2017 The Author(s) 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.

Symplectic id: 

819444

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article