Uncertainty relation and black-hole entropy of NUT-Kerr-Newman space-time

Abstract

In this paper, by using the quantum-statistical method and the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we directly obtain the partition function of the Bose field and the Fermi field on the background of the axisymmetrical NUT-Kerr-Newman black hole. Then we calculate the entropy of the Bose field and the Fermi field of the black hole near the horizon. And it is obtained that the entropy of the black hole is proportional to the area of the horizon. The inherent contact between the entropy of the black hole and the area of the horizon is opened out. It is shown the entropy of the black hole is the entropy of the quantum state on the surface of the horizon. The entropy is a quantum effect. The fact that the state density diverges near the horizon is removed by introducing the generalized uncertainty relation showing that the brick-wall method is related to quantization of the quantum field.