### 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) |
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Pages (from-to) | 937-949 |

Number of pages | 13 |

Journal | Communications in Mathematical Physics |

Volume | 359 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2018 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Galloway, G. J., Ling, E., & Sbierski, J. (2018). Timelike Completeness as an Obstruction to C

^{0}-Extensions.*Communications in Mathematical Physics*,*359*(3), 937-949. https://doi.org/10.1007/s00220-017-3019-2