Quasinormal modes and quantization of area/entropy for noncommutative BTZ black hole

Abstract

We investigate the quasinormal modes and area/entropy spectrum for the noncommutative BTZ black hole. The exact expressions for QNM frequencies are presented by expanding the noncommutative parameter in horizon radius. We find that the noncommutativity does not affect conformal weights (h_{L}, h_{R}), but it influences the thermal equilibrium. The intuitive expressions of the area/entropy spectrum are calculated in terms of Bohr–Sommerfeld quantization, and our results show that the noncommutativity leads to a nonuniform area/entropy spectrum. We also find that the coupling constant xi , which is the coupling between the scalar and the gravitational fields, shifts the QNM frequencies but not influences the structure of area/entorpy spectrum.