Low regularity approach to Bartnik's conjecture
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910742580559872 |
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| author | Flores, José Luis Herrera, Jónatan Solis, Didier A. |
| author_facet | Flores, José Luis Herrera, Jónatan Solis, Didier A. |
| contents | In this work we establish a version of the Bartnik Splitting Conjecture in the context of Lorentzian length spaces. In precise terms, we show that under an appropriate timelike completeness condition, a globally hyperbolic Lorentzian length space of the form $Σ\times \mathbb{R}$ with $Σ$ compact splits as a metric Lorentzian product, provided it has non negative timelike curvature bounds. This is achieved by showing that the causal boundary of that Lorentzian length space consists on a single point. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_08967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low regularity approach to Bartnik's conjecture Flores, José Luis Herrera, Jónatan Solis, Didier A. Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics In this work we establish a version of the Bartnik Splitting Conjecture in the context of Lorentzian length spaces. In precise terms, we show that under an appropriate timelike completeness condition, a globally hyperbolic Lorentzian length space of the form $Σ\times \mathbb{R}$ with $Σ$ compact splits as a metric Lorentzian product, provided it has non negative timelike curvature bounds. This is achieved by showing that the causal boundary of that Lorentzian length space consists on a single point. |
| title | Low regularity approach to Bartnik's conjecture |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2412.08967 |