Supersymmetric AdS_4 black holes and attractors

TL;DR

This work constructs the first genuine BPS black holes in $AdS_4$ with nonconstant scalar fields within $N=2$, $D=4$ gauged supergravity and analyzes their attractor behavior. By employing the timelike BPS classification and exploring multiple prepotentials (including STU variants and SU(1,n) models), it presents explicit static, supersymmetric solutions with various charge configurations and horizon geometries, deriving their near-horizon structures and entropies. A key finding is the frequent appearance of flat directions in the black hole potential, where horizon moduli are not fully fixed by charges, yet the entropy remains solely determined by the charges, consistent with an AdS attractor mechanism. The paper also provides a general near-horizon framework that extends attractor equations to gauged supergravity and illustrates how moduli spaces can arise even in BPS configurations, with implications for AdS/CFT and microscopic entropy counting.

Abstract

Using the general recipe given in arXiv:0804.0009, where all timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets were classified, we construct the first examples of genuine supersymmetric black holes in AdS_4 with nonconstant scalar fields. This is done for various choices of the prepotential, amongst others for the STU model. These solutions permit to study the BPS attractor flow in AdS. We also determine the most general supersymmetric static near-horizon geometry and obtain the attractor equations in gauged supergravity. As a general feature we find the presence of flat directions in the black hole potential, i.e., generically the values of the moduli on the horizon are not completely specified by the charges. For one of the considered prepotentials, the resulting moduli space is determined explicitely. Still, in all cases, we find that the black hole entropy depends only on the charges, in agreement with the attractor mechanism.