Static BPS black holes in AdS4 with general dyonic charges

We complete the study of static BPS, asymptotically AdS(4) black holes within N = 2 FI-gauged supergravity and where the scalar manifold is a symmetric very special Kahler manifold. We find the analytic form for the general solution to the BPS equations, the horizon appears as a double root of a particular quartic polynomial whereas in previous work this quartic polynomial further factored into a pair of double roots. A new and distinguishing feature of our solutions is that the phase of the supersymmetry parameter varies throughout the black hole. The general solution has 2n(v) independent parameters; there are two algebraic constraints on 2n(v) + 2 charges, matching our previous analysis on BPS solutions of the form AdS(2) x Sigma(g). As a consequence we have proved that every BPS geometry of this form can arise as the horizon geometry of a BPS AdS(4) black hole. When specialized to the STU-model our solutions uplift to M-theory and describe a stack of M2-branes wrapped on a Riemman surface in a Calabi-Yau fivefold with internal angular momentum.