Overspinning BTZ black holes with test particles and fields

It has been claimed that in a test of an asymptotically anti-de Sitter version of weak cosmic censorship conjecture by attempting to overspin a Baados, Teitelboim, and Zanelli (BTZ) black hole with test particles, one finds that it is not possible to spin up the black hole past its extremal limit. The result of this analysis is restricted to the case where the initial black hole is extremal. We extend this analysis to find that massive test particles can overspin the black hole, if we start with a nearly extremal black hole, instead. We also consider the interaction of the BTZ black hole with test fields. We show that overspinning of nearly extremal black holes is possible whether or not there is super-radiance for the field. If there is superradiance, overspinning occurs in a narrow range of frequencies bounded below by the super-radiant limit. However, if there is no super-radiance for the field, overspinning becomes generic and also applies to extremal black holes. This is in analogy with the Kerr case.