Limit curve theorems for incomplete metric spaces and the null distance on Lorentzian manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908638474403840 |
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| author | Rennie, Adam Whale, Ben |
| author_facet | Rennie, Adam Whale, Ben |
| contents | We prove a limit curve theorem for incomplete metric spaces. Our main application is to Sormani and Vegas' null distance, where our results give strong control on the Lorentzian lengths of limit curves. We also show that regular cosmological time functions and the surface function of a Cauchy surface in a globally hyperbolic manifold define such a null distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit curve theorems for incomplete metric spaces and the null distance on Lorentzian manifolds Rennie, Adam Whale, Ben Differential Geometry General Relativity and Quantum Cosmology Metric Geometry We prove a limit curve theorem for incomplete metric spaces. Our main application is to Sormani and Vegas' null distance, where our results give strong control on the Lorentzian lengths of limit curves. We also show that regular cosmological time functions and the surface function of a Cauchy surface in a globally hyperbolic manifold define such a null distance. |
| title | Limit curve theorems for incomplete metric spaces and the null distance on Lorentzian manifolds |
| topic | Differential Geometry General Relativity and Quantum Cosmology Metric Geometry |
| url | https://arxiv.org/abs/2511.05847 |