## Abstract

We produce new examples, both explicit and analytical, of bi-axisymmetric stationary vacuum black holes in five dimensions. A novel feature of these solutions is that they are asymptotically locally Euclidean, in which spatial cross-sections at infinity have lens space L(p, q) topology, or asymptotically Kaluza-Klein so that spatial cross-sections at infinity are topologically S ^{1} × S ^{2} . These are nondegenerate black holes of cohomogeneity 2, with any number of horizon components, where the horizon cross-section topology is any one of the three admissible types: S ^{3} , S ^{1} × S ^{2} , or L(p, q). Uniqueness of these solutions is also established. Our method is to solve the relevant harmonic map problem with prescribed singularities, having target symmetric space SL(3, R)/SO(3). In addition, we analyze the possibility of conical singularities and find a large family for which geometric regularity is guaranteed.

Original language | English |
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Article number | 053E01 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2018 |

Issue number | 5 |

DOIs | |

State | Published - 1 May 2018 |