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

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 considered. Here $\varepsilon = - 1$ corresponds to a ghost scalar field. These solutions are defined up to solutions of two master equations for two moduli functions, when $\lambda^2_i \neq 1/2$ for $\varepsilon = - 1$. Some physical parameters of the solutions are obtained: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters $\beta$ and $\gamma$. The PPN parameters do not depend on the couplings $\lambda_i$ and $\varepsilon$. A set of bounds on the gravitational mass and scalar charge are found by using a certain conjecture on the parameters of solutions, when $1 +2 \lambda_i^2 \varepsilon > 0$, $i =1,2$.