Quasinormal modes and phase transition of black holes

We have studied the scalar field as well as the fermionic field perturbations in the background of the massless BTZ black holes. Comparing with the perturbation results in the generic non-rotating BTZ black hole background, we found that the massless BTZ hole contains only normal modes in the perturbations. We argued that this special property reflects that the massless BTZ black hole is a different phase from that of the generic non-rotating BTZ hole.