Gedanken Experiments to Destroy a BTZ Black Hole

We consider Wald's type of gedanken experiments to destroy an extremal or near-extremal BTZ black hole in 3-dimensional torsional Mielke-Barkler gravity by throwing matter into the horizon. Provided the null energy condition for the falling matter, we prove the following—( i ) in MB model, an extremal BTZ black hole can be overspun and becomes a naked conical singularity, as long as the coupling coefficients in the theory live in a certain region of the parameter space; ( ii ) in 3-dimensional Einstein gravity and chiral gravity, which are two special limits of MB model , an extremal BTZ black hole cannot be overspun; and ( iii ) in both Einstein gravity and chiral gravity, a near-extremal BTZ black hole cannot be overspun, thus weak cosmic censorship is preserved. Wald's type of gedanken experiment provides an operational procedure of proving the third law of black hole mechanics. Through the AdS/CFT correspondence, our results on BTZ black holes also indicate that a third law of thermodynamics holds for the holographic CFTs dual to 3-dimensional Einstein gravity and chiral gravity.