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

TL;DR

This paper provides a simplified proof of the $C^0$-inextendibility of the maximal Schwarzschild spacetime, utilizing recent results on timelike geodesics in $C^0$-extensions and offering new structural insights.

Contribution

It introduces a more streamlined proof of Schwarzschild spacetime inextendibility, leveraging recent theorems and new boundary structure results.

Findings

Simplified proof of $C^0$-inextendibility for Schwarzschild spacetime

Use of recent results on timelike geodesics in $C^0$-extensions

New structural result for the boundary of globally hyperbolic spacetimes

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.