Dyon-like black hole solutions in the model with two Abelian gauge fields

TL;DR

This paper reviews dilatonic black hole solutions with two gauge fields in a 4D model, analyzing their properties, special integrable cases, and physical parameters like mass, temperature, and charges, including bounds and conjectures.

Contribution

It provides a comprehensive overview of dyon-like black hole solutions with two Abelian gauge fields, including new integrable cases linked to Lie algebras and physical parameter analysis.

Findings

Derived expressions for mass, scalar charge, temperature, and entropy.

Identified integrable cases corresponding to specific Lie algebras.

Proposed bounds on gravitational mass and scalar charge.

Abstract

Dilatonic black hole dyon-like solutions in the gravitational $4d$ model with a scalar field, two 2-forms, two dilatonic coupling constants $\lambda_i \neq 0$, $i =1,2$, obeying $\lambda_1 \neq - \lambda_2$ and the sign parameter $\varepsilon = \pm 1$ for scalar field kinetic term are overviewed. Here $\varepsilon = - 1$ corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when $\lambda^2_i \neq 1/2$ for $\varepsilon = - 1$. Several integrable cases corresponding to Lie algebras $A_1 + A_1$, $A_2$, $B_2 = C_2$ and $G_2$ are considered. Some physical parameters of the solutions are derived: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and PPN parameters $\beta$ and $\gamma$. Bounds on the gravitational mass and scalar charge (based on a certain conjecture) are presented.