On Uniqueness of supersymmetric Black holes in AdS(5)

TL;DR

This paper investigates the uniqueness and possible configurations of supersymmetric black holes in five-dimensional gauged supergravity, combining local and non-local methods to analyze horizon topologies and charge parameters.

Contribution

It extends previous analyses by incorporating non-local solution properties to constrain black hole topologies and parameters in AdS(5) supergravity.

Findings

No additional spherical black hole solutions beyond known ones.

Ring topology black holes, if they exist, are limited to three parameters.

Derived constraints on black hole parameters related to chemical potentials.

Abstract

We study the possibility of having 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 result obtained by local supersymmetry analysis but include the input coming from non-local properties of the solutions, like the attractor mechanism, the entropy function of Sen, the Euclidean formulation and general properties of the uplift to ten dimension. For the spherical case, we found that there is no room for more general Black holes than the ones already describe in 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 article, 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.