Holographic uniformization and black hole attractors

We establish an attractor mechanism for the horizon metric of asymptotically locally AdS(4) supersymmetric black holes. The horizon is a smooth Riemann surface with arbitrary metric at asymptotic infinity which is fixed to the constant curvature metric in the near horizon region. We show how this mechanism is realized for four-dimensional N = 2 gauged supergravity coupled to vector multiplets by focusing on the STU model. A similar analysis is performed for gauged supergravity theories in five, six, and seven dimen- sions where we establish the same mechanism by extending previous results on holographic uniformization.