Some Aspects of Spherical Symmetric Extremal Dyonic Black Holes in 4d N=1 Supergravity

TL;DR

This paper investigates extremal spherical symmetric black hole solutions in 4d N=1 supergravity, analyzing scalar field behavior, asymptotic geometries, and near horizon structures, including explicit models with superpotentials.

Contribution

It provides new insights into scalar field configurations and geometries of extremal black holes in N=1 supergravity, including existence proofs and explicit model examples.

Findings

Asymptotic geometries have non-zero scalar curvature and are generally not Einstein.

Existence of scalar fields interpolating between horizon and infinity.

Explicit ${ C}^{n}$-models with linear superpotential and gauge couplings.

Abstract

In this paper we study several aspects of extremal spherical symmetric black hole solutions of four dimensional N=1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and non-zero scalar curvature which are generally not Einstein. These spaces could also correspond to the near horizon geometries which are the product spaces of a two anti-de Sitter surface and the two sphere if the value of the scalars in both regions coincides. In addition, we prove the local existence of non-trivial radius dependent complex scalar fields which interpolate between the horizon and the asymptotic region. We finally give some simple ${\lC}^{n}$-models with both linear superpotential and gauge couplings.