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

TL;DR

The work addresses the construction of non-extremal dyon-like black holes in a 4D dilatonic model with two Abelian gauge fields and a scalar that may be ordinary or phantom. It derives two master equations for moduli functions and identifies integrable cases corresponding to Lie algebras $A_1+ A_1$, $A_2$, $B_2=C_2$, and $G_2$, providing explicit forms for the moduli, charges, and thermodynamic quantities. Key contributions include closed-form expressions for ADM mass, scalar charge, Hawking temperature, entropy, and PPN parameters, a special dependent-charge sector, and proposed universal mass/charge bounds based on a conjectured one-to-one mapping between charges and moduli. The results connect black hole physics with Toda-chain/Lie-algebra structures, yielding insights into no-hair-type bounds and the effect of dilatonic couplings and phantom fields on observable parameters.

Abstract

Dilatonic black hole dyon-like solutions in the gravitational $4d$ model with a scalar field, two 2-forms, two dilatonic coupling constants $λ_i \neq 0$, $i =1,2$, obeying $λ_1 \neq - λ_2$ 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 $λ^2_i \neq 1/2$ 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 $β$ and $γ$. Bounds on the gravitational mass and scalar charge (based on a certain conjecture) are presented.