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February 2018 The $C_0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian geometry
Jan Sbierski
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J. Differential Geom. 108(2): 319-378 (February 2018). DOI: 10.4310/jdg/1518490820

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. "The $C_0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian geometry." J. Differential Geom. 108 (2) 319 - 378, February 2018. https://doi.org/10.4310/jdg/1518490820

Information

Received: 22 July 2015; Published: February 2018
First available in Project Euclid: 13 February 2018

zbMATH: 06846980
MathSciNet: MR3763070
Digital Object Identifier: 10.4310/jdg/1518490820

Rights: Copyright © 2018 Lehigh University

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Vol.108 • No. 2 • February 2018
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