Canonical entropy of black hole

Abstract

Recently, Hawking radiation of the black hole was studied by tunnel effect method. It was found that the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How the deviation between the radiation spectrum from pure thermal spectrum affect the entropy is a very interesting problem. In this paper, we calculate the partition function using the energy spectrum derived by tunnel effect, then obtain the entropy of the black hole. When we take first order approximation, the logarithmic term of entropy correction is consistent with the one considering the generalized uncertainty relation. However, in our calculation, there is no uncertain factor. And the coefficient of logarithmic correction term is the same one after considering the correction to the black hole entropy due to the thermal fluctuation. There are no divergent terms in our result when the thermal capacity of the black hole is negative. So our discussion has universality.