Near-horizon geometries of supersymmetric AdS5 black holes

We provide a classification of near-horizon geometries of supersymmetric, asymptotically antide Sitter, black holes of five-dimensional U(1)-gauged supergravity which admit two rotational symmetries. We find three possibilities: a topologically spherical horizon, an S1×S2 horizon and a toroidal horizon. The near-horizon geometry of the topologically spherical case turns out to be that of the most general known supersymmetric, asymptotically anti-de Sitter, black hole of U(1)-gauged supergravity. The other two cases are parameterised by constant scalars and only exist in particular regions of this moduli space – in particular they do not exist within minimal gauged supergravity. We also find a solution corresponding to the near-horizon geometry of a three-charge supersymmetric black ring held in equilibrium by a conical singularity; when lifted to type IIB supergravity this solution can be made regular, resulting in a discrete family of warped AdS3 geometries. Analogous results are presented in U(1) n gauged supergravity.