Dilatonic dyon black hole solutions

TL;DR

This paper explores dilatonic dyon black hole solutions with arbitrary coupling, deriving physical parameters, bounds, and showing PPN parameters are independent of scalar coupling and sign, extending previous bounds and verifying them numerically.

Contribution

It introduces a general framework for dilatonic dyon black holes with arbitrary coupling and scalar sign, deriving new bounds and physical parameters, and extending previous results to broader cases.

Findings

PPN parameters are independent of scalar coupling and sign.

Derived bounds on gravitational mass and scalar charge.

Numerical verification of bounds for specific examples.

Abstract

Dilatonic black hole dyon solutions with arbitrary dilatonic coupling constant $\lambda \neq 0$ and canonical sign $\varepsilon = +1$ for scalar field kynetic term are considered. These solutions are defined up to solutions of two master equations for moduli funtions. For $\lambda^2 \neq 1/2$ the solutions are extended to $\varepsilon = \pm 1$, where $\varepsilon = -1$ corresponds to ghost (phantom) scalar field. Some physical parameters of the solutions: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters $\beta$ and $\gamma$ are obtained. It is shown that PPN parameters do not depend on scalar field coupling $\lambda$ and $\varepsilon$. Two group of bounds on gravitational mass and scalar charge (for fixed and arbitrary extremality parameter $\mu >0$) are found by using a certain conjecture on parameters of solutions when $1 +2 \lambda^2 \varepsilon > 0$. These bounds are verified numerically for certain examples. By product we are led to well-known lower bound on mass which was obtained earlier by Gibbons, Kastor, London, Townsend and Traschen by using spinor techniques.