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.

arXiv comment12 pages

References in corpus (24)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem
• When conceptual worlds collide: The GUP and the BH entropy
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Interpretation of Quantum Field Theories with a Minimal Length Scale
• Entropy for dilatonic black hole
• Black hole entropy without brick walls
• Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle
• On the Entropy of a Quantum Field in the Rotating Black Holes
• Electromagnetic fields in Schwarzschild and Reissner-Nordström geometry. Quantum corrections to the black hole entropy
• Action and entropy of black holes in spacetimes with a cosmological constant
• Entropy of the Schwarzschild black hole to all orders in the Planck length
• Positivity of Entropy in the Semi-Classical Theory of Black Holes and Radiation
• Entropy of the Randall-Sundrum brane world with the generalized uncertainty principle
• Entropy of Reissner-Nordstrom Black Holes with Minimal Length Revisited
• Mass and charge fluctuations and black hole entropy
• The Generalized Uncertainty Principle and Corrections to the Cardy-Verlinde Formula in $SAd{S}_5$ Black Holes
• Canonical entropy of three-dimensional BTZ black hole
• Entropy of a charged black hole in two dimensions without cutoff
• Logarithmic corrections to three-dimensional black holes and de Sitter spaces
• Quantum entropy of the general non-extreme stationary axisymmetric black hole due to minimally coupled quantum scalar field
• A Note on Quantum Field Theories with a Minimal Length Scale
• Scalar Field Contribution to Rotating Black Hole Entropy
• General Logarithmic Corrections to Bekenstein-Hawking Entropy

Cited by in corpus (5)

• Modified dispersion relations in extra dimensions
• The Generalized Uncertainty Principle and the Friedmann equations
• Condensation of an ideal gas with intermediate statistics on the horizon
• Bound of Noncommutativity Parameter Based on Black Hole Entropy
• Entropy and temperatures of Nariai black hole