A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry

David Katona

doi:10.1007/s00023-024-01415-4

paper

A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry

arXiv:2306.09933 · doi:10.1007/s00023-024-01415-4

Abstract

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 $R^{3}$ 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 $R^{3}$ 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.

arXiv commentv2: 54 pages; accepted version. Remarks and references added, typos corrected, results unchanged

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