Rotating Topological Black Holes

TL;DR

This paper introduces new rotating topological black hole solutions in anti-de Sitter space, including higher genus and toroidal types, with unique geometric and causal properties.

Contribution

It presents explicit metrics for rotating black holes with non-spherical horizons derived from known solutions via isometries and analytical continuation.

Findings

Higher genus black holes lack global axial symmetry.

Toroidal black holes have bounded rotation related to their mass.

New solutions expand the landscape of known topological black holes.

Abstract

A class of metrics solving Einstein's equations with 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 blackholes appear to be simpler, they have rotational symmetry and the amount of rotation they can have is bounded by some power of the mass.