Overcharging a nonsingular black hole in general relativity: the nonlinear electrodynamic field effects

Abstract: The Ay\'on-Beato Garc\'ia (ABG) solution describes a nonlinear electrodynamic nonsingular black hole in general relativity and can be regarded as a strong field correction to the Reissner-Nordstr\"om solution. We exam the possibility of destroying the ABG nonsingular black hole with a test charged particle and a complex scalar field. By comparing with the results of gadenken experiment to destroy the Reissner-Nordstr\"om black hole, we get the nonlinear electrodynamic field effects on the destruction of the event horizon. We obtain the parameter regions of the particle and scalar field, which allow us to destroy the event horizon of an extremal and near-extremal ABG black hole. Our findings show that both can be destroyed due to nonlinear electrodynamic effects. Interestingly, the parameter intervals for the charged particle and scalar field needed to destroy the event horizon of an extremal black hole are identical. Since the ABG black hole is nonsingular, our results remain consistent with the weak cosmic censorship conjecture and may offer a means to explore the interior of a black hole.