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 (, ) we show that below the Compton wavelength the black hole solutions reduce to that of Reissner-Nordstr\"om via the Vainshtein mechanism in the weak-field limit. In the simplest case with ==0 the solution exhibits the van Dam-Veltman-Zakharov discontinuity but ordinary general relativity is recovered deep inside the horizon due to the existence of electric charge, though this case is observationally excluded. For 0 and =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 and are both nonzero, there exist two branches of solutions depending on the positivity of. When 0 the metric factors exhibit only small corrections compared to the solutions obtained in general relativity, and under a particular choice of =^2/6 the standard Reissner-Nordstr\"om-de Sitter solution is recovered.