Universal spinning black holes and theories of class R

We study a supersymmetric, rotating, electrically charged black hole in AdS₄ which is a solution of four-dimensional minimal gauged supergravity. Using holography we show that the free energy on S³ and the superconformal index of the dual three-dimensional N = 2 SCFT, in the planar limit, are related in a simple universal way. This result applies to large classes of SCFTs constructed from branes in string and M-theory which we discuss in some detail. For theories of class R, which arise from N M5-branes wrapped on hyperbolic three-manifolds, we show that the superconformal index agrees with the black hole entropy in the large N limit.