On the uniqueness of continuous spacetime extensions in 1+1 dimensions with applications to weak null singularities
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914161303224320 |
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| author | Cameron, Peter Sbierski, Jan |
| author_facet | Cameron, Peter Sbierski, Jan |
| contents | Motivated by weak null singularities in black hole interiors, we study 1+1 dimensional Lorentzian manifolds $(M,g)$ which admit a continuous spacetime extension across a null boundary $v=0$, where $v<0$ is a null coordinate. We study the degree to which such extensions are unique up to the boundary. Firstly, we find that in general not even the $C^0$-structure of the extension is uniquely determined by the assumption that the metric extends continuously. However, we exhibit an interesting local-global relation regarding the $C^0$-structure which in particular entails its rigidity for ''strongly spherically symmetric'' continuous extensions across the Cauchy horizon of the Reissner-Nordström spacetime. Secondly, we construct continuous extensions which have the same $C^0$-structure, but do not have equivalent $C^1$-structures. This construction also carries over to weak null singularities in 3+1 dimensions. Understanding the uniqueness properties of continuous spacetime extensions to the boundary is of importance for the study of low-regularity inextendibility problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13422 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the uniqueness of continuous spacetime extensions in 1+1 dimensions with applications to weak null singularities Cameron, Peter Sbierski, Jan General Relativity and Quantum Cosmology Differential Geometry Motivated by weak null singularities in black hole interiors, we study 1+1 dimensional Lorentzian manifolds $(M,g)$ which admit a continuous spacetime extension across a null boundary $v=0$, where $v<0$ is a null coordinate. We study the degree to which such extensions are unique up to the boundary. Firstly, we find that in general not even the $C^0$-structure of the extension is uniquely determined by the assumption that the metric extends continuously. However, we exhibit an interesting local-global relation regarding the $C^0$-structure which in particular entails its rigidity for ''strongly spherically symmetric'' continuous extensions across the Cauchy horizon of the Reissner-Nordström spacetime. Secondly, we construct continuous extensions which have the same $C^0$-structure, but do not have equivalent $C^1$-structures. This construction also carries over to weak null singularities in 3+1 dimensions. Understanding the uniqueness properties of continuous spacetime extensions to the boundary is of importance for the study of low-regularity inextendibility problems. |
| title | On the uniqueness of continuous spacetime extensions in 1+1 dimensions with applications to weak null singularities |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2511.13422 |