Analysis of Black Hole Entropy in Brick Wall Model
Masakatsu Kenmoku, Kamal Kanti Nandi, Kazuyasu Shigemoto · arXiv (Cornell University) · 2005
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 $\\delta $ with respect to the brick wall cut-off $\\epsilon $. The leading contribution to entropy for non-extreme case $(\\delta \ eq 0)$ is shown to satisfy the area law with quadratic divergence with respect to the invariant cut-off $\\epsilon_{{\\rm inv}}$ while the extreme case $(\\delta =0)$ exhibits logarithmic divergence or constant value with respect to $\\epsilon $. The general formula is applied to Reissner-Nordstr\\"{o}m, dilaton and brane-world black holes and we obtain consistent results.