BPS Black Hole Horizons in N=2 Gauged Supergravity

TL;DR

This paper derives explicit solutions for BPS black hole horizons in four-dimensional N=2 gauged supergravity, including scalar fields, metrics, and entropy, with applications to M-theory embeddings and dyonic charges.

Contribution

It provides the general solution to BPS horizon equations in N=2 gauged supergravity with symplectic covariance, including explicit solutions for symmetric spaces and implicit solutions for general models.

Findings

Explicit solutions for symmetric special Kahler manifolds.

Implicit solutions involving holomorphic quadratic equations.

New horizon geometries with dyonic charges in M-theory contexts.

Abstract

We study static BPS black hole horizons in four dimensional N=2 gauged supergravity coupled to $n_v$-vector multiplets and with an arbitrary cubic prepotential. We work in a symplectically covariant formalism which allows for both electric and magnetic gauging parameters as well as dyonic background charges and obtain the general solution to the BPS equations for horizons of the form $AdS_2\times \Sigma_g$. In particular this means we solve for the scalar fields as well as the metric of these black holes as a function of the gauging parameters and background charges. When the special Kahler manifold is a symmetric space, our solution is completely explicit and the entropy is related to the familiar quartic invariant. For more general models our solution is implicit up to a set of holomorphic quadratic equations. For particular models which have known embeddings in M-theory, we derive new horizon geometries with dyonic charges and numerically construct black hole solutions. These correspond to M2-branes wrapped on a Riemann surface in a local Calabi-Yau five-fold with internal spin.