Timelike completeness as an obstruction to $C^0$-extensions
General Relativity and Quantum Cosmology
2017-12-06 v4 Differential Geometry
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 -inextendible. For the proof we make use of the result, recently established by S\"amann [17], that even for \emph{continuous} Lorentzian manifolds that are globally hyperbolic, there exists a length-maximizing causal curve between any two causally related points.
Keywords
Cite
@article{arxiv.1704.00353,
title = {Timelike completeness as an obstruction to $C^0$-extensions},
author = {Gregory J. Galloway and Eric Ling and Jan Sbierski},
journal= {arXiv preprint arXiv:1704.00353},
year = {2017}
}
Comments
v2: pertinent citations added and minor changes, v3: small refinements and improvements; theorem added, v4: added figure, minor changes, version accepted for publication in CMP