Rotating Topological Black Holes

TL;DR

The paper constructs exact rotating topological black holes in anti-de Sitter gravity by analytically continuing the Kerr–de Sitter solution, yielding g>1 genus horizons without global axial symmetry and a rotating, yet simpler toroidal case with well-defined mass and angular momentum. The g>1 solutions exhibit intricate causal structures and horizon warping, while the toroidal solution maintains a global rotational symmetry and provides concrete quasi-local charges. Together, these results broaden the landscape of AdS black holes with nontrivial topology and offer a framework to study their thermodynamics and potential connections to string theory. The work highlights the role of horizon topology in gravitational dynamics and the nuanced definitions of conserved quantities in non-asymptotically flat spacetimes.

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.