Abstract: Using the quantum statistical method, the difficulty of solving wave equation on the background of the black hole is avoided. We directly solve the partition functions of bosonic field and fermionic field on the background of the axisymmetric Kerr black hole through using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity theory. Then the entropy of the bosonic field and fermionic field near the horizon of the black hole are calculated. In our results the divergence appearing in the brick wall model is removed, as well as without using the small mass approximation. The series expression of the statistical entropy of the black hole is convergent. Therefore, it gives a better understanding of the black hole statistical entropy in non-spherical symmetry spacetimes.

Keywords: 
• quantum statistics /
• non-spherical symmetry spacetimes /
• generalized uncertainty relation /
• black hole entropy