A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910653151707136 |
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| author | Katona, David |
| author_facet | Katona, David |
| contents | We extend the recent classification of five-dimensional, supersymmetric asymptotically flat black holes with only a single axial symmetry to black holes with Kaluza-Klein asymptotics. This includes a similar class of solutions for which the supersymmetric Killing field is generically timelike, and the corresponding base (orbit space of the supersymmetric Killing field) is of multi-centred Gibbons-Hawking type. These solutions are determined by four harmonic functions on $\mathbb{R}^3$ with simple poles at the centres corresponding to connected components of the horizon, and fixed points of the axial symmetry. The allowed horizon topologies are $S^3$, $S^2\times S^1$, and lens space $L(p, 1)$, and the domain of outer communication may have non-trivial topology with non-contractible 2-cycles. The classification also reveals a novel class of supersymmetric (multi-)black rings for which the supersymmetric Killing field is globally null. These solutions are determined by two harmonic functions on $\mathbb{R}^3$ with simple poles at centres corresponding to horizon components. We determine the subclass of Kaluza-Klein black holes that can be dimensionally reduced to obtain smooth, supersymmetric, four-dimensional multi-black holes. This gives a classification of four-dimensional asymptotically flat supersymmetric multi-black holes first described by Denef et al. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09933 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry Katona, David High Energy Physics - Theory General Relativity and Quantum Cosmology We extend the recent classification of five-dimensional, supersymmetric asymptotically flat black holes with only a single axial symmetry to black holes with Kaluza-Klein asymptotics. This includes a similar class of solutions for which the supersymmetric Killing field is generically timelike, and the corresponding base (orbit space of the supersymmetric Killing field) is of multi-centred Gibbons-Hawking type. These solutions are determined by four harmonic functions on $\mathbb{R}^3$ with simple poles at the centres corresponding to connected components of the horizon, and fixed points of the axial symmetry. The allowed horizon topologies are $S^3$, $S^2\times S^1$, and lens space $L(p, 1)$, and the domain of outer communication may have non-trivial topology with non-contractible 2-cycles. The classification also reveals a novel class of supersymmetric (multi-)black rings for which the supersymmetric Killing field is globally null. These solutions are determined by two harmonic functions on $\mathbb{R}^3$ with simple poles at centres corresponding to horizon components. We determine the subclass of Kaluza-Klein black holes that can be dimensionally reduced to obtain smooth, supersymmetric, four-dimensional multi-black holes. This gives a classification of four-dimensional asymptotically flat supersymmetric multi-black holes first described by Denef et al. |
| title | A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2306.09933 |