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

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.