On a class of 4D Kaehler bases and AdS5 supersymmetric black holes

We construct a class of toric Kaehler manifolds, M4, of real dimension four, a subset of which corresponds to the Kaehler bases of all known 5D asymptotically AdS5 supersymmetric black-holes. In a certain limit, these Kaehler spaces take the form of cones over Sasaki spaces, which, in turn, are fibrations over toric manifolds of real dimension two. The metric on M4 is completely determined by a single function H(x), which is the conformal factor of the two dimensional space. We study the solutions of minimal five dimensional gauged supergravity having this class of Kaehler spaces as base and show that in order to generate a five dimensional solution H(x) must obey a simple sixth order differential equation. We discuss the solutions in detail, which include all known asymptotically AdS5 black holes as well as other spacetimes with non-compact horizons. Moreover we find an infinite number of supersymmetric deformations of these spacetimes with less spatial isometries than the base space. These deformations vanish at the horizon, but become relevant asymptotically