Logarithmic terms in brick wall model

We clarify the relation between black hole entropy and quantum field spin. Starting from the Newman-Penrose formalism, we derive the Teukolsky-type master equation governing massless fields of arbitrary spin s⩽2 in the Kerr-Newman-de Sitter spacetime. Then using the 't Hooft's brick wall model, we calculate the entropy of the black hole due to the quantum fields by the WKB approximation on the Teukolsky-type master equation. In particular, we carefully deal with the logarithmic term contribution to the entropy. It is shown that the term not only depends on the characteristics of the metric and the quadratic term of quantum field spin but also on the linear term of quantum field spin. This is very different from the result obtained earlier. All results of the present work are valid for the Schwarzschild, Reissner-Nordström, Kerr, Kerr-Newman, and de Sitter spacetime background, or any combination of these.