Weak cosmic censorship conjecture for the (2+1)-dimensional charged BTZ black hole in the Einstein-Gauss-Bonnet Gravity

TL;DR

This paper investigates whether the weak cosmic censorship conjecture holds for charged BTZ black holes in Einstein-Gauss-Bonnet gravity, finding that they can be overcharged, thus violating the conjecture in this modified gravity context.

Contribution

It demonstrates that the weak cosmic censorship conjecture can be violated for charged BTZ black holes within Einstein-Gauss-Bonnet gravity, extending previous results to this modified theory.

Findings

Charged BTZ black holes can be overcharged in EGB gravity.

Violation of the weak cosmic censorship conjecture in EGB theory.

Negative minimum energy at the horizon for extremal and near-extremal black holes.

Abstract

It is well known that ($2+1$) dimensional charged BTZ (Banados, Teitelboim, Zanelli) black hole can be overcharged by a charged scalar field and a charged particle in contrast to their analogues in ($3+1$) and higher dimensions. In this regard, it may play an important role to understand more deeply the properties of the ($2+1$)-dimensional charged black hole in the Einstein-Gauss-Bonnet (EGB) gravity. In this paper, we test the validity of the weak cosmic censorship conjecture for the ($2+1$)-dimensional charged black hole in novel EGB theory derived recently by Henniger et. al (2021). We show that the minimum energy that particle can have at the horizon becomes negative for both an extremal and nearly-extremal BTZ black holes in EGB gravity. It is proven that both extremal and nearly-extremal $(2+1)$ dimensional BTZ black hole could be overcharged in EGB theory, leading to the violation of the weak cosmic censorship conjecture (WCCC), which is in good agreement with the results obtained for the classical BTZ black hole.