Charged black holes in nonlinear massive gravity

We find static charged black hole solutions in nonlinear massive gravity. In the parameter space of two gravitational potential parameters $(α, β)$ we show that below the Compton wavelength the black hole solutions reduce to that of Reissner-Nordström via the Vainshtein mechanism in the weak field limit. In the simplest case with $α=β=0$ the solution exhibits the vDVZ discontinuity but ordinary General Relativity is recovered deep inside the horizon due to the existence of electric charge. For $α\neq0$ and $β=0$, the post-Newtonian parameter of the charged black hole evolves to that of General Relativity via the Vainshtein mechanism within a macroscopic distance; however, a logarithmic correction to the metric factor of the time coordinate is obtained. When $α$ and $β$ are both nonzero, there exist two branches of solutions depending on the positivity of $β$. When $β<0$, the strong coupling of the scalar graviton weakens gravity at distances smaller than the Vainshtein radius. However, when $β>0$ the metric factors exhibit only small corrections compared to the solutions obtained in General Relativity, and under a particular choice of $β=α^2/6$ the standard Reissner-Nordström-de Sitter solution is recovered.

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