The $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian geometry
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...
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| Format: | Journal article |
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International Press
2018
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| _version_ | 1797095064870060032 |
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| author | Sbierski, J |
| author_facet | Sbierski, J |
| author_sort | Sbierski, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:22:42Z |
| format | Journal article |
| id | oxford-uuid:cb916380-8e0d-4aa3-aca1-3a62dca561f9 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:22:42Z |
| publishDate | 2018 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:cb916380-8e0d-4aa3-aca1-3a62dca561f92022-03-27T07:15:43ZThe $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian geometryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cb916380-8e0d-4aa3-aca1-3a62dca561f9Symplectic Elements at OxfordInternational Press2018Sbierski, JThe 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. |
| spellingShingle | Sbierski, J The $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian geometry |
| title | The $C^0$-inextendibility of the Schwarzschild spacetime and the
spacelike diameter in Lorentzian geometry |
| title_full | The $C^0$-inextendibility of the Schwarzschild spacetime and the
spacelike diameter in Lorentzian geometry |
| title_fullStr | The $C^0$-inextendibility of the Schwarzschild spacetime and the
spacelike diameter in Lorentzian geometry |
| title_full_unstemmed | The $C^0$-inextendibility of the Schwarzschild spacetime and the
spacelike diameter in Lorentzian geometry |
| title_short | The $C^0$-inextendibility of the Schwarzschild spacetime and the
spacelike diameter in Lorentzian geometry |
| title_sort | c 0 inextendibility of the schwarzschild spacetime and the spacelike diameter in lorentzian geometry |
| work_keys_str_mv | AT sbierskij thec0inextendibilityoftheschwarzschildspacetimeandthespacelikediameterinlorentziangeometry AT sbierskij c0inextendibilityoftheschwarzschildspacetimeandthespacelikediameterinlorentziangeometry |