Numerical Modeling of Charged Black Holes with Massive Dilaton

In this paper the static, spherically symmetric and electrically charged black hole solutions in Einstein-Born-Infeld gravity with massive dilaton are investigated numerically. The Continuous Analog of Newton Method (CANM) is used to solve the corresponding nonlinear multipoint boundary value problems (BVPs). The linearized BVPs are solved numerically by means of collocation scheme of fourth order. A special class of solutions are the extremal ones. We show that the extremal horizons within the framework of the model satisfy some nonlinear system of algebraic equations. Depending on the charge $q$ and dilaton mass $\gamma$, the black holes can have no more than three horizons. This allows us to construct some Hermite polynomial of third order. Its real roots describe the number, the type and other characteristics of the horizons.