Null distance and convergence of Lorentzian length spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912007106592768 |
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| author | Kunzinger, Michael Steinbauer, Roland |
| author_facet | Kunzinger, Michael Steinbauer, Roland |
| contents | The null distance of Sormani and Vega encodes the manifold topology as well as the causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length spaces, the analog of (metric) length spaces, which generalize Lorentzian causality theory beyond the manifold level. We then study Gromov-Hausdorff convergence based on the null distance in warped product Lorentzian length spaces and prove first results on its compatibility with synthetic curvature bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_05393 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Null distance and convergence of Lorentzian length spaces Kunzinger, Michael Steinbauer, Roland Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Metric Geometry 53C23, 53C50, 53B30, 51K10, 53C80 The null distance of Sormani and Vega encodes the manifold topology as well as the causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length spaces, the analog of (metric) length spaces, which generalize Lorentzian causality theory beyond the manifold level. We then study Gromov-Hausdorff convergence based on the null distance in warped product Lorentzian length spaces and prove first results on its compatibility with synthetic curvature bounds. |
| title | Null distance and convergence of Lorentzian length spaces |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Metric Geometry 53C23, 53C50, 53B30, 51K10, 53C80 |
| url | https://arxiv.org/abs/2106.05393 |