Can the induced increase in the angular velocity prevent the overspinning of BTZ black holes?

Abstract: Previously we showed that nearly extremal Ba~{n}ados-Teitelboim-Zanelli (BTZ) black holes can be overspun by test bodies and fields, following the work of Rocha and Cardoso for the extremal case. The naked singularities in AdS space-times correspond to states rotating faster than light in the Ads/CFT correspondence. Therefore, overspinning turns out to be a drastic problem in a (2+1) dimensional AdS space-time, where one cannot invoke backreaction effects. Here, we consider the induced increase in the angular velocity of the event horizon which modifies the condition to allow the absorption of the perturbations satisfying the null energy condition. We show that its magnitude is sufficiently large to prevent the absorption of the challenging modes both for test bodies and scalar fields. We bring a solution to the notorious overspinning problem which does not involve any reference to self-energy or gravitational radiation.