Non-Extreme Black Holes of Five Dimensional N=2 AdS Supergravity

TL;DR

The paper analyzes non-extreme static black holes in five-dimensional N=2 gauged supergravity using very special geometry, showing that gauging modifies the non-extremality function by a term proportional to the gauge coupling g^2, which can produce naked singularities in the BPS limit. It provides a detailed STU-model solution, derives the ADM mass, and establishes a lower bound on the non-extremality parameter μ to guarantee regular horizons; the extremal non-supersymmetric limit features zero temperature with finite entropy. The results extend the understanding of AdS/CFT backgrounds with reduced supersymmetry and suggest analogous behavior in D=4 gauged supergravity. The STU solution serves as a concrete gravity background with potential implications for holographic studies of strongly coupled gauge theories.

Abstract

We derive and analyse the full set of equations of motion for non-extreme static black holes (including examples with the spatial curvatures k=-1 and k=0) in D=5 N=2 gauged supergravity by employing the techniques of "very special geometry". These solutions turn out to differ from those in the ungauged supergravity only in the non-extremality function, which has an additional term (proportional to the gauge coupling g), responsible for the appearance of naked singularities in the BPS-saturated limit. We derive an explicit solution for the STU model of gauged supergravity which is incidentally also a solution of D=5 N=4 and N=8 gauged supergravity. This solution is specified by three charges, the asymptotic negative cosmological constant (minimum of the potential) and a non-extremality parameter. While its BPS-saturated limit has a naked singularity, we find a lower bound on the non-extremality parameter (or equivalently on the ADM mass) for which the non-extreme solutions are regular. When this bound is saturated the extreme (non-supersymmetric) solution has zero Hawking temperature and finite entropy. Analogous qualitative features are expected to emerge for black hole solutions in D=4 gauged supergravity as well.