Matter-coupled supersymmetric Kerr-Newman-${\mathrm{AdS}}_4$ black holes

We present new analytic rotating four-dimensional anti–de Sitter space (${\mathrm{AdS}}_4$) black holes, found as solutions of gauged $\mathcal{N}=2$ supergravity coupled to Abelian vector multiplets with a symmetric scalar manifold. These configurations preserve two real supercharges and have a smooth limit to the BPS Kerr-Newman-${\mathrm{AdS}}_4$ black hole. We spell out the solution of the $STU$ model admitting an uplift to M-theory on ${\mathrm{S}}^7$. We identify an entropy function, which upon extremization gives the black hole entropy, to be holographically reproduced by the leading $N$ contribution of the generalized superconformal index of the dual theory.