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

Dilatonic black hole dyon-like solutions in the gravitational $4d$ model with a scalar field, two 2-forms, two dilatonic coupling constants ${\lambda }_i\mathrm{\ne }0$, $i=1,2$, obeying ${\lambda }_1\mathrm{\ne }-{\lambda }_2$ and the sign parameter $\epsilon =\pm 1$ for scalar field kinetic term are overviewed. Here $\epsilon =-1$ corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when ${\lambda }_i^2\mathrm{\ne }1\mathrm{/}2$ for $\epsilon =-1$. 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.