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

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.

12 pages

References in corpus (7)

• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Entropy of the Schwarzschild black hole to all orders in the Planck length
• Entropy of Reissner-Nordstrom Black Holes with Minimal Length Revisited
• Canonical entropy of three-dimensional BTZ black hole
• Entropy of a charged black hole in two dimensions without cutoff
• A Note on Quantum Field Theories with a Minimal Length Scale
• General Logarithmic Corrections to Bekenstein-Hawking Entropy