Sub-leading contributions to the black hole entropy in the brick wall approach
Harish-Chandra Research Institute, Allahabad.
We compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher orders (in fact, up to the sixth order in \hbar) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. We find that, in four dimensions, the corrections to the Bekenstein-Hawking entropy are of the form (A^n log A), whereas, in six dimensions, they behave as (A^m + A^n log A), where A denotes the area of the black hole event horizon, and (m, n) < 1. We compare our results with the corrections to the Bekenstein-Hawking entropy that have been obtained through other approaches in the literature and highlight the agreements and differences.