Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification

TL;DR

This paper classifies critical points of the black hole potential in $ ext{N}=2$, $D=4$ supergravity with $U(1)$ Fayet-Iliopoulos gaugings, analyzing their properties and presenting a new extremal black hole solution in the $STU$ model.

Contribution

It provides a comprehensive classification of attractor points, generalizes entropy expressions using special K"ahler geometry, and introduces a novel extremal black hole solution.

Findings

Classification of critical points for spherical and hyperbolic horizons.

Generalized entropy formulas for symmetric scalar manifolds.

New extremal black hole solution with dilaton interpolation.

Abstract

We classify the critical points of the effective black hole potential which governs the attractor mechanism taking place at the horizon of static dyonic extremal black holes in $\mathcal{N}=2$, $D=4$ Maxwell-Einstein supergravity with $U(1)$ Fayet-Iliopoulos gaugings. We use a manifestly symplectic covariant formalism, and we consider both spherical and hyperbolic horizons, recognizing the relevant sub-classes to which some representative examples belong. We also exploit projective special K\"{a}hler geometry of vector multiplets scalar manifolds, the $U$-duality-invariant quartic structure (and 2-polarizations thereof) in order to retrieve and generalize various expressions of the entropy of asymptotically AdS$_{4}$ BPS black holes, in the cases in which the scalar manifolds are symmetric spaces. Finally, we present a novel static extremal black hole solution to the $STU$ model, in which the dilaton interpolates between an hyperbolic near-horizon geometry and AdS$_{4}$ at infinity.