Entropy of a quantum field in rotating black holes

Abstract

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., ${\Omega }_0={\Omega }_H$) do the free energy and entropy become divergent at the event horizon. In the Hartle-Hawking state the leading terms of the entropy are $A\left(\frac{1}{h}\right)+B\ln \mathrm{}\left(h\right)+\mathrm{finite}$, where $h$ is the cutoff in the radial coordinate near the horizon. In terms of the proper distance cutoff $\epsilon$ it is written as $S=\frac{N{A}_H}{{\epsilon }^2}$. The origin of the divergence is that the density of states on the stationary surface and beyond it diverges.