Barrow black holes and the minimal length

TL;DR

This paper explores the fractal structure of black hole horizons, deriving a logarithmic entropy form and analyzing thermodynamic stability and unique heat capacity behaviors for various black hole types.

Contribution

It introduces a fractal horizon model leading to a new entropy formula and examines thermodynamic properties of different black holes.

Findings

Black hole entropy has a logarithmic form similar to Boltzmann entropy.

Black holes studied are thermodynamically stable with positive heat capacities.

RN-AdS black hole exhibits Schottky anomaly-like behavior in heat capacity.

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{\"o}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.