On the proof of the $C^0$-inextendibility of the Schwarzschild spacetime

Abstract

This article presents a streamlined version of the author's original proof of the $C^0$-inextendibility of the maximal analytic Schwarzschild spacetime. Firstly, we deviate from the original proof by using the result, recently established in collaboration with Galloway and Ling, that given a $C^0$-extension of a globally hyperbolic spacetime, one can find a timelike geodesic that leaves this spacetime. This result much simplifies the proof of the inextendibility through the exterior region of the Schwarzschild spacetime. Secondly, we give a more flexible and shorter argument for the inextendibility through the interior region. Furthermore, we present a small new structural result for the boundary of a globally hyperbolic spacetime within a $C^0$-extension which serves as a new and simpler starting point for the proof.

Prepared for submission to the proceedings of the meeting "Non-Regular Spacetime Geometry", Florence, 20.6.-22.6.2017. Based on arXiv:1507.00601, v2: minor changes, version accepted for publication

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