Local uniqueness of the Black String with small circle size
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915357134946304 |
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| author | Albertini, Emma Platt, Daniel |
| author_facet | Albertini, Emma Platt, Daniel |
| contents | In this article we study uniqueness of the Black String, i.e. the product of 4-dimensional Schwarzschild space with a circle of length L.
In arXiv:2410.20967, this was reduced to a non-linear elliptic PDE, and we use this setup to show that for small L the Black String is infinitesimally rigid as a Ricci-flat metric.
Using a fixed point theorem, we prove that this implies local uniqueness, i.e. there exist no other Ricci-flat metrics near the Black String, and we give bounds for the size of the neighborhood in which the Black String is unique.
We compare this with the toy problem of a scalar field satisfying an elliptic equation that was already solved in arXiv:2410.20967 using different methods.
In this case we can use the fixed point theorem method to prove not just a local but a global statement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local uniqueness of the Black String with small circle size Albertini, Emma Platt, Daniel High Energy Physics - Theory General Relativity and Quantum Cosmology In this article we study uniqueness of the Black String, i.e. the product of 4-dimensional Schwarzschild space with a circle of length L. In arXiv:2410.20967, this was reduced to a non-linear elliptic PDE, and we use this setup to show that for small L the Black String is infinitesimally rigid as a Ricci-flat metric. Using a fixed point theorem, we prove that this implies local uniqueness, i.e. there exist no other Ricci-flat metrics near the Black String, and we give bounds for the size of the neighborhood in which the Black String is unique. We compare this with the toy problem of a scalar field satisfying an elliptic equation that was already solved in arXiv:2410.20967 using different methods. In this case we can use the fixed point theorem method to prove not just a local but a global statement. |
| title | Local uniqueness of the Black String with small circle size |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.04573 |