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

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 metri...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.4310/jdg/1518490820

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Magdalen College
Role:
Author
Publisher:
International Press Publisher's website
Journal:
Journal of Differential Geometry Journal website
Volume:
108
Issue:
2
Pages:
319-378
Publication date:
2018-02-13
Acceptance date:
2016-05-31
DOI:
EISSN:
1945-743X
ISSN:
0022-040X
Pubs id:
pubs:829015
URN:
uri:cb916380-8e0d-4aa3-aca1-3a62dca561f9
UUID:
uuid:cb916380-8e0d-4aa3-aca1-3a62dca561f9
Local pid:
pubs:829015

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