Rotating attractors and BPS black holes in AdS4

We analyze stationary BPS black hole solutions to 4dN = 2 abelian gauged supergravity. Using an appropriate near horizon ansatz, we construct rotating attractors with magnetic flux realizing a topological twist along the horizon surface, for any theory with a symmetric scalar manifold. An analytic flow to asymptotically locally AdS(4) is presented for a subclass of these near-horizon geometries, and an explicit new example of supersymmetric AdS(4) rotating black hole is discussed in detail. We further note that, upon tuning the gauging to special values, one can obtain solutions with different asymptotics, and in particular reductions of doubly spinning asymptotically AdS(5) black holes. Finally we present a proposal for the form of the BPS entropy function with rotation, which we expect to be holographically related to the refined twisted index of the dual theory.