Rotating topological black holes

A class of metrics solving Einstein's equations with a negative cosmological constant and representing rotating, topological black holes is presented. All such solutions are in the Petrov type-$D$ class, and can be obtained from the most general metric known in this class by acting with suitably chosen discrete groups of isometries. First, by analytical continuation of the Kerr--de Sitter metric, a solution describing uncharged, rotating black holes whose event horizon is a Riemann surface of arbitrary genus $g>1,$ is obtained. Then a solution representing a rotating, uncharged toroidal black hole is also presented. The higher genus black holes appear to be quite exotic objects; they lack global axial symmetry and have an intricate causal structure. The toroidal black holes appear to be simpler; they have rotational symmetry and the amount of rotation they can have is bounded by some power of the mass.

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