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

Sbierski, J

1 February 2018

Journal:

Journal of Differential Geometry

Last Updated:

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

2

108

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.

829015

Submitted

Journal Article