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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.14567 |
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| _version_ | 1866909603138109440 |
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| author | Aksteiner, Steffen Andersson, Lars Dahl, Mattias Nilsson, Gustav Simon, Walter |
| author_facet | Aksteiner, Steffen Andersson, Lars Dahl, Mattias Nilsson, Gustav Simon, Walter |
| contents | Uniqueness results for asymptotically locally flat and asymptotically flat $S^1$-symmetric gravitational instantons are proved using a divergence identity of the type used in uniqueness proofs for static black holes, combined with results derived from the $G$-signature theorem. Our results include a proof of the $S^1$-symmetric version of the Euclidean Black Hole Uniqueness conjecture, a uniqueness result for the Taub-bolt family of instantons, as well as a proof that an ALF $S^1$-symmetric instanton with the topology of the Chen-Teo family of instantons is Hermitian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14567 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gravitational instantons with $S^1$ symmetry Aksteiner, Steffen Andersson, Lars Dahl, Mattias Nilsson, Gustav Simon, Walter Differential Geometry General Relativity and Quantum Cosmology 53C25 Uniqueness results for asymptotically locally flat and asymptotically flat $S^1$-symmetric gravitational instantons are proved using a divergence identity of the type used in uniqueness proofs for static black holes, combined with results derived from the $G$-signature theorem. Our results include a proof of the $S^1$-symmetric version of the Euclidean Black Hole Uniqueness conjecture, a uniqueness result for the Taub-bolt family of instantons, as well as a proof that an ALF $S^1$-symmetric instanton with the topology of the Chen-Teo family of instantons is Hermitian. |
| title | Gravitational instantons with $S^1$ symmetry |
| topic | Differential Geometry General Relativity and Quantum Cosmology 53C25 |
| url | https://arxiv.org/abs/2306.14567 |