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.

10 pages, 5 figures

References in corpus (10)

• The Area of a Rough Black Hole
• Barrow holographic dark energy
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• 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
• Generalized entropies and corresponding holographic dark energy models
• Thermodynamics of a black hole based on a generalized uncertainty principle
• Barrow black hole corrected-entropy model and Tsallis nonextensivity
• Barrow's black hole entropy and the equipartition theorem
• Cosmological constant as confining U(1) charge in two-dimensional dilaton gravity

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• 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