The thin film model without cutoff and the black hole entropy of Dirac field

The physical idea of thin film model improved from brick-wall model is more direct and clearer than brick-wall model and gives prominence to the significance of the event horizon serving as the characteristic surface of a static or stationary black hole. To remove the divergence of the density of states, an ultraviolet cutoff factor is also introduced into the thin film model. The cutoff is introduced artificially and it has not been understood clearly up to now. There is an indication in a reference that the divergence can be removed without any cutoff when the generalized uncertainty relation is used to calculate black hole entropy. In this paper, thin film model without cutoff and the essential difference between the thin film model without cutoff and the thin film model with cutoff are expounded by the example of calculating the entropy of spherically symmetric static black hole Dirac field.