Hausdorff-type metric geometry of the space of Cauchy hypersurfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914469704105984 |
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| author | Lange, Christian Peteranderl, Jonas W. |
| author_facet | Lange, Christian Peteranderl, Jonas W. |
| contents | We equip the space of Cauchy hypersurfaces in a globally hyperbolic spacetime with a natural Hausdorff-type metric and study its properties, in particular completeness and local compactness, for Lorentzian manifolds and in more general synthetic Lorentzian settings. For this purpose, we also generalize results on completeness properties of spacetimes due to Beem and Takahashi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11783 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hausdorff-type metric geometry of the space of Cauchy hypersurfaces Lange, Christian Peteranderl, Jonas W. Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Metric Geometry We equip the space of Cauchy hypersurfaces in a globally hyperbolic spacetime with a natural Hausdorff-type metric and study its properties, in particular completeness and local compactness, for Lorentzian manifolds and in more general synthetic Lorentzian settings. For this purpose, we also generalize results on completeness properties of spacetimes due to Beem and Takahashi. |
| title | Hausdorff-type metric geometry of the space of Cauchy hypersurfaces |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Metric Geometry |
| url | https://arxiv.org/abs/2604.11783 |