Overcharging process around a magnetized black hole: can the backreaction effect of magnetic field restore cosmic censorship conjecture?

Abstract

It is well known that the electrically charged Reissner-Nordstr\"{o}m black hole could be overcharged. Here, we investigate the process of overcharging of a magnetized Reissner-Nordstr\"{o}m black hole that includes effect of the magnetic field generated by own magnetic charge of source on the background geometry. It is found that magnetic field prevents a transition to occur from black hole to naked singularity, thus overcharging cannot be attained which happens due to the fact that the magnetic field reaches its threshold value. It turns out that beyond threshold value the magnetic field can exert large Lorentz force on particles and dominate over the gravitational force, allowing charged particles not to fall into the black hole. One may conclude, there occurs no evidence for violation of cosmic censorship conjecture for a magnetized Reissner-Nordstr\"{o}m black hole beyond threshold value of the magnetic field.