Black Holes in Models with Dilaton Field and Electric or Electric and Magnetic Charges

TL;DR

This paper presents exact static spherically symmetric charged black hole solutions in four dimensions with dilaton fields, including purely electric and dyonic cases, highlighting their properties and compliance with energy conditions.

Contribution

It provides new explicit solutions for charged black holes with dilaton fields, extending previous models by including both electric and magnetic charges with detailed parameter analysis.

Findings

Solutions are asymptotically flat with two horizons and a singularity at r=0.

The electric-only solution has three free parameters: mass, electric charge, and an additional parameter.

Dyonic solutions are characterized by three free parameters: mass, magnetic charge, and an extra parameter.

Abstract

Exact static spherically symmetric charged black holes in four dimensions are presented. One of them has only electric charge and another electric and magnetic charges. In these solutions the metric is asymptotically flat, has two horizons, irremovable singularity only at $r=0$, and the dilaton field is singular only at $r=0$. The solution with electric charge only is characterized by three free parameters, the ADM mass, the electric charge and an additional free parameter. It can be considered as a modification of the GHS-GM solution obtained by changing the coupling between dilaton and electromagnetic field. The general dyonic solution is again characterized by three free parameters, the ADM mass, the magnetic charge and an additional free parameter, which is not the electric charge. According to a definition of the no-hair conjecture the solutions are "hairy".A very interesting special case of the dyonic solution is characterized by three free parameters, the ADM mass and the electric and the magnetic charges. The solutions satisfy the dominant as well as the strong energy condition outside and on the external horizon.