### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1-13 |

Number of pages | 13 |

Journal | Communications in Mathematical Physics |

DOIs | |

State | Accepted/In press - Nov 5 2017 |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

^{0}-Extensions.

*Communications in Mathematical Physics*, 1-13. https://doi.org/10.1007/s00220-017-3019-2

**Timelike Completeness as an Obstruction to C ^{0}-Extensions.** / Galloway, Gregory J; Ling, Eric; Sbierski, Jan.

Research output: Contribution to journal › Article

^{0}-Extensions',

*Communications in Mathematical Physics*, pp. 1-13. https://doi.org/10.1007/s00220-017-3019-2

^{0}-Extensions. Communications in Mathematical Physics. 2017 Nov 5;1-13. https://doi.org/10.1007/s00220-017-3019-2

}

TY - JOUR

T1 - Timelike Completeness as an Obstruction to C0-Extensions

AU - Galloway, Gregory J

AU - Ling, Eric

AU - Sbierski, Jan

PY - 2017/11/5

Y1 - 2017/11/5

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.

UR - http://www.scopus.com/inward/record.url?scp=85033459992&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033459992&partnerID=8YFLogxK

U2 - 10.1007/s00220-017-3019-2

DO - 10.1007/s00220-017-3019-2

M3 - Article

AN - SCOPUS:85033459992

SP - 1

EP - 13

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -