Testing Cosmic Censorship Conjecture for Extremal and Near-extremal (2+1)-dimensional MTZ Black Holes

TL;DR

This paper investigates whether extremal and near-extremal (2+1)-dimensional MTZ black holes can be overcharged by test particles, finding that while first-order effects suggest overcharging is possible, second-order effects uphold the weak cosmic censorship conjecture.

Contribution

The study demonstrates that second-order perturbations prevent overcharging of nearly-extremal MTZ black holes, supporting the weak cosmic censorship conjecture in (2+1) dimensions.

Findings

Extremal (2+1)-D black holes can be overcharged by test particles at first order.

Nearly-extremal black holes can be overcharged ignoring second-order effects.

Second-order perturbations prevent overcharging, upholding cosmic censorship.

Abstract

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, Teitelboim, and Zanelli (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 $4$ and higher dimensions. Nearly-extremal black holes can also be overcharged, by a judicious choice of energy and charge for the test particles in the case when we ignore the second order effects. Contrary to this, nearly-extremal black holes cannot be overcharged by the second order perturbation, obeying the weak cosmic censorship conjecture.