Overcharging black holes and cosmic censorship in Born-Infeld gravity

The Born-Infeld gravity is a modification of the theory of general relativity inspired by the nonlinear Born-Infeld electrodynamics. The theory is described by a series of higher curvature terms added to the Einstein-Hilbert action with the parameter ?. The Born-Infeld gravity has several interesting exact neutral and charged black hole solutions. We study the problem of overcharging extremal black hole solutions of Born-Infeld gravity using a charged test particle to create naked singularity. We show that unlike general relativity, the overcharging could be possible for a charged extremal black hole in Born-Infeld gravity as long as the matter sector is described by usual Maxwell's electrodynamics. Once the matter sector is also modified in accordance to the Born-Infeld prescription with the parameter b, the overcharging is not possible as long as the parameters obey the condition 4?b2?1.