Overcharging black holes and cosmic censorship in Eddington-inspired Born-Infeld gravity

TL;DR

This paper investigates the possibility of overcharging extremal black holes in Eddington-inspired Born-Infeld (EiBI) gravity, revealing conditions under which naked singularities can form, contrasting with general relativity.

Contribution

It demonstrates that overcharging extremal black holes in EiBI gravity depends on the matter sector, showing that modifications to matter fields can prevent naked singularity formation.

Findings

Overcharging is possible in EiBI gravity with Maxwell electrodynamics.

Modifying matter fields to Born-Infeld electrodynamics prevents overcharging.

Parameter condition $4 \kappa b^2 \\leq 1$ ensures no overcharging occurs.

Abstract

The Eddington-inspired Born-Infeld (EiBI) 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 $\kappa$. The EiBI gravity has several interesting exact neutral and charged black hole solutions. We study the problem of overcharging extremal black hole solutions of EiBI 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 EiBI 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 $4 \kappa b^2 \leq 1$.