Rotating 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 Kerrde 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 *

Rotating black branes wrapped on Einstein spaces

“…where now (6) reduces to the one found in [7] as a stationary generalization of four-dimensional topological black holes. In this case a few comments are in order.…”

“…Now the metrics (2) and (6) are not the end of the story. It is known [7] (see also below) that for d = 4 they emerge as a special case of the most general Petrov-type D metric found by Plebanski and Demianski [11]. This, in turn, contains other black objects as subcases, e. g. a four-dimensional rotating cylindrical AdS black hole [7].…”

“…In this case a few comments are in order. First of all, the statement in [7], that the (θ, φ) sector can be compactified to obtain Riemann surfaces of genus g by identifying opposite sites of a regular geodesic 4g-gon centered at the origin (θ, φ) = (0, 0), is not true. To see this, consider a fundamental region chosen so that the mid-point of one geodesic segment is at (θ, φ) = (θ 0 , 0).…”

“…It is known [7] (see also below) that for d = 4 they emerge as a special case of the most general Petrov-type D metric found by Plebanski and Demianski [11]. This, in turn, contains other black objects as subcases, e. g. a four-dimensional rotating cylindrical AdS black hole [7]. Besides, in view of the fact that the horizon of d-dimensional static topological AdS black holes is not necessarily a space of constant curvature, but can be an arbitrary Einstein space [12]…”

“…Now already in four dimensions there is a variety of black configurations apart from the Kerr-AdS solution. A class of such objects was presented in [7] as stationary generalizations of so-called topological black holes. In the present paper we shall find higher-dimensional versions of these solutions, generalizing the d-dimensional Kerr-AdS metric recently found in [5] to arbitrary topologies.…”