Entropy of the BTZ black hole in 2+1 dimensions

We semi-classically calculate the entropy of a scalar field in the background of the BTZ black hole, and derive the perimeter law of the entropy. The proper length from the horizon to the ultraviolet cutoff is independent of both the mass and the angular momentum of the black hole. It is shown that the superradiant scattering modes give the sub-leading order contribution to the entropy while the non-superradiant modes give the leading order one, and thus superradiant effect is minor.