Statistical Entropy Based on the Generalized-Uncertainty-Principle-Induced Effective Metric

Abstract

We investigate the statistical entropy of black holes within the framework of the generalized uncertainty principle (GUP) by employing effective metrics that incorporate leading-order and all-orders quantum gravitational corrections. We construct three distinct effective metrics induced by the GUP, which are derived from GUP-corrected temperature, entropy, and all-orders GUP corrections, and analyze their impact on black hole entropy using 't Hooft's brick wall method. Our results show that, despite the differences in the effective metrics and the corresponding ultraviolet cutoffs, the statistical entropy consistently satisfies the Bekenstein-Hawking area law when expressed in terms of an invariant (coordinate-independent) distance near the horizon. Furthermore, we demonstrate that the GUP naturally regularizes the ultraviolet divergence in the density of states, eliminating the need for artificial cutoffs and yielding finite entropy even when counting quantum states only in the vicinity of the event horizon. These findings highlight the universality and robustness of the area law under GUP modifications and provide new insights into the interplay between quantum gravity effects and black hole thermodynamics.

14 pages

References in corpus (34)

• Quantum Geometry and Black Hole Entropy
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• Universality of Quantum Gravity Corrections
• Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
• On Gravity and the Uncertainty Principle
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Hawking Radiation as Tunneling through the Quantum Horizon
• Generalized Uncertainty Principle: Approaches and Applications
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Gravitational tests of the Generalized Uncertainty Principle
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
• On Hawking Radiation as Tunneling with Logarithmic Corrections
• Black hole entropy without brick walls
• Generalised Uncertainty Principle, Remnant Mass and Singularity Problem in Black Hole Thermodynamics
• Gravitational Uncertainty and Black Hole Remnants
• Entropy of the Schwarzschild black hole to all orders in the Planck length
• Generalized uncertainty principles and localization in discrete space
• Black holes thermodynamics to all orders in the Planck length in extra dimensions
• Entropy of the Randall-Sundrum brane world with the generalized uncertainty principle
• Entropy of a charged black hole in two dimensions without cutoff
• Quantum-corrected scattering and absorption of a Schwarzschild black hole with GUP
• Derivations of group rings
• Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy
• Linear and Quadratic GUP, Liouville Theorem, Cosmological Constant, and Brick Wall Entropy
• The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
• Remnant mass and entropy of black holes and modified uncertainty principle
• A Critique on Some Aspects of GUP Effective Metric
• New generalized uncertainty principle with parameter adaptability for the minimum length
• Lifshitz scalar, brick wall method, and GUP in Hořava-Lifshitz Gravity
• Effective geometries and generalized uncertainty principle corrections to the Bekenstein-Hawking entropy
• GUP corrected entropy of the Schwarzschild black hole in holographic massive gravity
• Gravitational Observations and LQGUP
• Tidal effects based on GUP-induced effective metric