Testing cosmic censorship conjecture for extremal and near-extremal (2 + 1)-dimensional MTZ black holes

We test the validity of the weak cosmic censorship conjecture for the (2 + 1)-dimensional charged anti-de Sitter black hole solution, which was derived by Martinez et al (MTZ). We first construct a thought experiment by throwing test charged particles on an extremal MTZ black hole. We derive that extremal (2 + 1) dimensional black holes can be overcharged by test particles, unlike their analogues in (3 + 1) and higher dimensions. Nearly-extremal MTZ black holes can also be overcharged, by a judicious choice of energy and charge for the test particles when the second order effects are ignored. We also incorporate the second order effects for nearly extremal MTZ black holes by adapting the method developed by Sorce and Wald. However it turns out that the second order effects cannot compensate for the overcharging of MTZ black holes.