Timelike completeness as an obstruction to $\textit{C}$$^{0}$-Extensions

19 Feb 2018

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 S ̈amann [17], that even for continuous Lorentzian manifolds that are globally hyperbolic, there exists a length-maximizing causal curve between any two causally related points.