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arXiv · 1507.00601

The $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian Geometry

Jan Sbierski
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Abstract

The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that it is even inextendible as a Lorentzian manifold with a continuous metric. To capture the obstruction to continuous extensions through the curvature singularity, we introduce the notion of the spacelike diameter of a globally hyperbolic region of a Lorentzian manifold with a merely continuous metric and give a sufficient condition for the spacelike diameter to be finite. The investigation of low-regularity inextendibility criteria is motivated by the strong cosmic censorship conjecture.

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Jan Sbierski. 2015-07-02. The $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian Geometry. https://arxiv.org/abs/1507.00601

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