Barrow black holes and the minimal length

Abstract

Following Barrow's idea of fractal black hole horizon, we re-derive black hole entropy of static spherically symmetric black holes. When a black hole absorbs matter its horizon area will increase. Given the spherically fractal structure, we conjecture that the minimal increase of the horizon area should be the area of the smallest bubble sphere. From this, we find the black hole entropy has a logarithmic form, which is similar to that of Boltzmann entropy if we consider $A/A_{pl}$ as the number of microscopic states. We further calculate temperatures and heat capacities of Schwarzschild, Reissner-Nordstr{ö}m(RN), and RN-AdS black holes. It is found that their temperatures are all monotonically increasing and the heat capacities are all positive, which means these black holes are thermodynamically stable. Besides, for RN-AdS black hole we find its heat capacity has Schottky anomaly-like behavior, which may reflect the existence of the discrete energy level and restricted microscopical degree of freedom.

arXiv comment10 pages, 5 figures

References in corpus (24)

• Quantum gravity and minimum length
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• The Area of a Rough Black Hole
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• When conceptual worlds collide: The GUP and the BH entropy
• Barrow holographic dark energy
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Generalized Uncertainty Principle: Approaches and Applications
• The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
• Black hole thermodynamics with generalized uncertainty principle
• Quantum corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle
• Corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle
• Generalized entropies and corresponding holographic dark energy models
• Black hole thermodynamics with generalized uncertainty principle
• Thermodynamics of a black hole based on a generalized uncertainty principle
• GUP parameter and black hole temperature
• Barrow black hole corrected-entropy model and Tsallis nonextensivity
• Barrow's black hole entropy and the equipartition theorem
• Schottky Anomaly of deSitter Black Holes
• Cosmological constant as confining U(1) charge in two-dimensional dilaton gravity
• Specific Heats and Schottky Peaks for Black Holes in Extended Thermodynamics
• Maximally localized states and quantum corrections of black hole thermodynamics in the framework of a new generalized uncertainty principle

Cited by in corpus (6)

• Barrow holographic dark energy with Granda-Oliveros cut-off
• Equilibrium Temperature for Black Holes with Nonextensive Entropy
• Barrow's non-linear charged Anti-de Sitter black hole and stability
• The $D$-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy
• Finite geometry and black hole stability: Embedding discrete space into classical manifolds
• Thermodynamics of Barrow Einstein-power-Yang-Mills AdS black hole in the restricted phase space