Destroying MTZ black holes with test particles

Neglecting the self-force and radiative effects, we follow the spirit of Wald's gedanken experiment and discuss whether a (2+1)-dimensional Martinez-Teitelboim-Zanelli (MTZ) black hole can turn into a naked singularity by capturing a charged and massive particle. We find that after capturing a charged and massive test particle, an extremal or near-extremal MTZ black hole could turn into naked singularity, leading to a possible violation of the cosmic censorship. There exist ranges of the test particles' energies △E which allow the appearance of naked singularities from both extremal and near extremal MTZ black holes.