Scalar field contribution to rotating black hole entropy

The scalar field contribution to entropy is studied in an arbitrary $D$ dimensional one parameter rotating spacetime by semiclassical methods. By introducing a zenith angle dependent cutoff parameter, the generalized area law is derived. The nonrotating limit can be taken smoothly and it yields known results. The derived area law is then applied to the Bañados-Teitelboim-Zanelli black hole in $(2+1)$ dimensions and the Kerr-Newman black hole in $(3+1)$ dimensions. The generalized area law is reconfirmed by the Euclidean path integral method for the quantized scalar field. The scalar field mass contribution is discussed briefly.