Anti-De Sitter BPS Black Holes in N=2 Gauged Supergravity

TL;DR

The paper constructs static electric BPS black holes in $D=4$, $N=2$ gauged supergravity with vector multiplets that asymptote to $AdS_4$, expressing solutions in terms of holomorphic sections of special geometry. By requiring vanishing gravitino and gaugino variations, it derives half-supersymmetry—preserving configurations and provides explicit forms for the metric, gauge fields, and the Killing spinor, with harmonic functions $H_I = abla_I + q_I/r$ and $A_t^I = e^{2U} Y^I$. The resulting solution is given by $ds^2 = - (e^{2U} + g^2 r^2 e^{-2U}) dt^2 + dr^2/(e^{2U} + g^2 r^2 e^{-2U}) + e^{2U} r^2 (dtheta^2 + sin^2 theta dphi^2)$ and $H_I = ext{const}+rac{q_I}{r}$, with $e^{-2U} = Z ar{Z}$ encoded in the holomorphic data. Notably, these static BPS AdS$_4$ electric black holes in gauged $N=2$ supergravity exhibit naked singularities, and the formalism remains valid without requiring a prepotential, offering a pathway to further non-extreme solutions.

Abstract

Electrically charged solutions breaking half of the supersymmetry in Anti-De Sitter four dimensional N=2 supergravity coupled to vector supermultiplets are constructed. These static black holes live in an asymptotic $AdS_4$ space-time. The Killing spinor, i. e., the spinor for supersymmetry variation is explicitly constructed for these solutions.