Charged BTZ black holes cannot be destroyed via the new version of the gedanken experiment

Abstract

The singularity at the center of charged Bañados–Teitelboim–Zanelli (BTZ) black holes is called a conical singularity. Unlike the canonical singularity in typical black holes, a conical singularity does not destroy the causality of spacetime. Due to the special property of the conical singularity, we examine the weak cosmic censorship conjecture (WCCC) using the new version of the gedanken experiment proposed by Sorce and Wald. A perturbation process wherein the spherically symmetric matter fields pass through the event horizon and fall into the black holes is considered. Assuming that the cosmological constant is obtained by the matter fields, it therefore can be seen as a dynamical variable during the process. From this perspective, according to the stability condition and the null energy condition, the first- and second-order perturbation inequalities are derived. Based on the first-order optimal condition and the second-order perturbation inequality, we show that the nearly extremal charged BTZ black hole cannot be destroyed in the above perturbation process. The result also implies that even if the singularity at the center of the black hole is conical, it still should be surrounded by the event horizon and hidden inside the black hole.