On the entropy of a quantum field in 2 + 1 dimensional spinning black holes

We calculate the entropy of a scalar field in a rotating black hole in 2 + 1 dimension. In the Hartle-Hawking state the entropy is proportional to the horizon area, but diverges linearly in h, where h is the radial cut-off. In the WKB approximation the superradiant modes do not contribute to the entropy.