Rotating black holes with Nil or SL(2, R) horizons

We construct rotating black holes in N = 2, D = 5 minimal and matter- coupled gauged supergravity, with horizons that are homogeneous but not isotropic. Such spaces belong to the eight Thurston model geometries, out of which we consider the cases Nil and SL(2, R). In the former, we use the recipe of [1] to directly rederive the solution that was obtained by Gutowski and Reall in [2] as a scaling limit from a spherical black hole. With the same techniques, the first example of a black hole with SL(2, R) horizon is constructed, which is rotating and one quarter BPS. The physical properties of this solution are discussed, and it is shown that in the near-horizon limit it boils down to the geometry of [2], with a supersymmetry enhancement to one half. Dimensional reduction to D = 4 gives a new solution with hyperbolic horizon to the t^3 model that carries both electric and magnetic charges. Moreover, we show how to get a nonextremal rotating Nil black hole by applying a certain scaling limit to Kerr-AdS(5) with two equal rotation parameters, which consists in zooming onto the north pole of the S^2 over which the S^3 is fibered, while boosting the horizon velocity effectively to the speed of light.