On the non-BPS first order flow in N=2 U(1)-gauged Supergravity

We consider theories of N=2 supergravity with Fayet-Iliopoulos gauging, and describe a procedure to obtain non-BPS extremal black hole solutions in asymptotically AdS_4 space, in a fully symplectic covariant framework. By considering both electric as well as magnetic gauging, we are able to find new extremal purely magnetic and dyonic solutions. We consistently impose the Dirac quantization condition as a constraint on the black hole and gravitinos charges. This additional requirement allows to parameterize the black hole entropy in terms of an integer and of the entropy of the corresponding black hole in the ungauged model. We also find the nonextremal generalization of the dyonic solution and we compute the product of the areas. For all the configurations with asymptotic supersymmetry we furthermore compute the mass.