Static supersymmetric black holes in AdS4 with spherical symmetry

Abstract

Abstract:We elaborate further on the static supersymmetric AdS 4 black holes found in [1], investigating thoroughly the BPS constraints for spherical symmetry in N = 2 gauged supergravity in the presence of Fayet-Iliopoulos terms. We find Killing spinors that preserve two of the original eight supercharges and investigate the conditions for genuine black holes free of naked singularities. The existence of a horizon is intimately related with the requirement that the scalars are not constant, but given in terms of harmonic functions in analogy to the attractor flow in ungauged supergravity. The black hole charges depend on the choice of the electromagnetic gauging, with only magnetic charges for purely electric gaugings. Finally we show how these black holes can be embedded in N = 8 supergravity and thus in M-theory.

On the non-BPS first order flow in $ \mathcal{N} $ = 2 U(1)-gauged Supergravity

“…Static regular black holes solutions in N = 2 U(1)-gauged Supergravity can be at most 1/4-BPS, and have been derived in [8,9,10]. We are going to consider the t 3 model described by a cubic prepotential.…”

“…where supersymmetry fixes the number n to be ±1 [9,10]. The non-BPS solutions, in general, do not satisfy the Dirac quantization condition, but they do satisfy, by construction, another relation.…”

“…These solution are purely magnetic: q 0 = q 1 = 0. We will first describe the 1/4 BPS solution found by [8] and [10], we then discuss the non-BPS solution generated by the procedure explained in Section 2.2. Finally we review the nonextremal generalization of the magnetic solution, already found in [11], and we comment on the product of the four areas.…”

“…Given the lack of a regular extremal configurations, properties such as the entropy-area law have not been extensively studied, and no further investigations on the zero temperature configurations have been carried out. Only recently, in fact, it has been shown that it is possible to have genuinely finite horizon black holes if one reduces the supersymmetry preserved by the solution to be 1/4 of the original vacuum [8,9,10]. This now opens the possibility of getting important insights on the physics of black holes in gauged supergravity, such as the microstate structure of the entropy of extremal black holes.…”

“…As we will see, for the non-BPS configurations we have to impose by hand the Dirac quantization condition. This provides us with a tower of extremal black holes for any integer n. We apply this solution generating technique to the solutions found in [9] and [10], namely for dyonic and purely magnetic black holes in presence of mixed and electric gaugings, respectively. They are actually equivalent configurations, since the frames in which they are constructed can be transformed one into the other by a symplectic transformation, followed by a holomorphic coordinate redefinition.…”