On the uniqueness of supersymmetric black holes in AdS(5)

We study the possibility of having a black hole of spherical and ring horizon topology with five independent charges in the U(1)³-model of 5D gauge supergravity. To study these possibilities we consider not only the known results obtained by local supersymmetry analysis but include the input from non-local properties of the solutions, such as the attractor mechanism, the entropy function of Sen, the Euclidean formulation and general properties of the uplift to ten dimensions. For the spherical case, we found that there is no room for more general black holes than those already described in Kunduri et al (2006 J. High Energy Phys. JHEP04(2006)036 (Preprint hep-th/0601156)). On the other hand, if a solution of ring horizon topology exists, we conclude that it must be labeled by three independent parameters only, since it has to satisfy two independent constraints that we explicitly find in terms of its chemical potentials. At the end of the paper, based on all the local and non-local information, we put forward a conjecture on the constraints that characterize general black holes dual to {\cal N}=4 SYM.