- Abstract:
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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...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted Manuscript
- Files:
-
-
(pdf, 582.8KB)
-
- Publisher copy:
- 10.4310/jdg/1518490820
-
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- 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:
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1945-743X
- ISSN:
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0022-040X
- Pubs id:
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pubs:829015
- URN:
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uri:cb916380-8e0d-4aa3-aca1-3a62dca561f9
- UUID:
-
uuid:cb916380-8e0d-4aa3-aca1-3a62dca561f9
- Local pid:
- pubs:829015
- Copyright holder:
- Jan Sbierski
- Copyright date:
- 2018
- Notes:
-
This is the accepted manuscript version of the article. The final version is available online from International Press at: https://doi.org/10.4310/jdg/1518490820
Journal article
The $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian geometry
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