Entropy of Kerr-Newman black hole to all orders in the Planck length

TL;DR

This paper calculates the entropy of Kerr-Newman black holes to all orders in the Planck length using a quantum statistical approach, avoiding traditional cutoffs and approximations, and provides a convergent series expansion for the entropy.

Contribution

It introduces a new method to compute black hole entropy directly from the partition function without cutoffs, applicable to non-spherical spacetimes.

Findings

Derived a convergent series expansion for black hole entropy.

Eliminated the need for cutoffs and mass approximations in entropy calculations.

Extended the quantum statistical entropy analysis to Kerr-Newman black holes.

Abstract

Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided.We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric Kerr-Newman black hole using the new equation of state density motivated by the generalized uncertainty principle in the quantum gravity. Then near the black hole horizon, we calculate entropies of Bose and Fermi field between the black hole horizon surface and the hypersurface with the same inherent radiation temperature measured by an observer at an infinite distance. In our results there are not cutoffs and little mass approximation introduced in the conventional brick-wall method. The series expansion of the black hole entropy is obtained. And this series is convergent. It provides a way for studying the quantum statistical entropy of a black hole in a non-spherical symmetric spacetime.