Entropy of a quantum field in rotating black holes

By using the brick wall method we calculate a free energy and the entropy of the scalar field in rotating black holes. As one approaches the stationary limit surface rather than the event horizon in a comoving frame, these become divergent. Only when the field is comoving with the black hole (i.e., Ω₀=ΩH) do the free energy and entropy become divergent at the event horizon. In the Hartle-Hawking state the leading terms of the entropy are A(1/h)+Bln(h)+finite, where h is the cutoff in the radial coordinate near the horizon. In terms of the proper distance cutoff ε it is written as S=NAHε². The origin of the divergence is that the density of states on the stationary surface and beyond it diverges.