Solution Independent Analysis of Black Hole Entropy in Brick Wall Model

Abstract

Using the brick wall regularization of 't Hooft, the entropy of non-extreme and extreme black holes is investigated in a general static, spherically symmetric spacetime. We classify the singularity in the entropy by introducing a {\it new} index $δ$ with respect to the brick wall cut-off $ε$. The leading contribution to entropy for non-extreme case $(δ\neq 0)$ is shown to satisfy the area law with quadratic divergence with respect to the invariant cut-off $ε_{\rm inv}$ while the extreme case $(δ=0)$ exhibits logarithmic divergence or constant value with respect to $ε$. The general formula is applied to Reissner-Nordström, dilaton and brane-world black holes and we obtain consistent results.