Improved black hole entropy calculation without cutoff

The brick wall model and thin film model are most representative models in black hole entropy calculation. However, each of them must have a cutoff in order to avoid the divergence, and the divergence itself cannot be explained satisfactorily. Li Xiang(6) substituted the classical uncertainty relation with the generalized uncertainty relation, the divergence was removed; consequently the cutoff was also removed. But due to the complex expression, he did not give the final solution. He only drew a conclusion that the upper bound of a black hole entropy is in proportional to its horizon area. The method using the generalized uncertainty relation to brick wall model is studied in depth. It is finally found out that the black hole entropy itself is also proportional to its horizon area instead of the upper bound.