The Entropy of the Complex Scalar Field in a Charged Kerr Black Hole

By using the brick wall method we calculate the thermodynamic potential of the complex scalar field in a charged Kerr black hole. Using it we show that in the Hartle-Hawking state the leading term of the entropy is proportional to $\frac{ A _H}{\epsilon^2}$, which becomes divergent as the system approaches the black hole horizon. The origin of the divergence is that the density of states diverges at the horizon.