The C<sup>0</sup>-inextendibility of the schwarzschild spacetime and the spacelike diameter in lorentzian geometry

Author: 

Sbierski, J

Publication Date: 

1 February 2018

Journal: 

Journal of Differential Geometry

Last Updated: 

2021-04-08T07:10:03.127+01:00

Issue: 

2

Volume: 

108

page: 

319-378

abstract: 

© 2018 Project Euclid. 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.

Symplectic id: 

829015

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article