Static supersymmetric black holes in AdS4 with spherical symmetry

We elaborate further on the static supersymmetric AdS4 black holes found in [1], investigating thoroughly the BPS constraints for spherical symmetry in N = 2 gauged supergravity in the presence of Fayet-Iliopoulos terms. We find Killing spinors that preserve two of the original eight supercharges and investigate the conditions for genuine black holes free of naked singularities. The existence of a horizon is intimately related with the requirement that the scalars are not constant, but given in terms of harmonic functions in analogy to the attractor flow in ungauged supergravity. The black hole charges depend on the choice of the electromagnetic gauging, with only magnetic charges for purely electric gaugings. Finally we show how these black holes can be embedded in N = 8 supergravity and thus in M-theory.