Barrow's non-linear charged Anti-de Sitter black hole and stability

TL;DR

This paper investigates the thermodynamics and stability of Barrow's non-linear charged Anti-de Sitter black holes, deriving their entropy, temperature, and heat capacity, revealing their thermodynamic stability and unique features like Schottky anomaly-like behavior.

Contribution

It re-derives the entropy of Barrow's EPYM AdS black hole, analyzes its thermodynamic properties, and uncovers stability conditions and novel phenomena such as Schottky anomaly-like behavior.

Findings

Black holes are thermodynamically stable within certain parameters.

The temperature ratio aligns with other Schwarzschild-like black holes.

Heat capacity exhibits Schottky anomaly-like behavior.

Abstract

As we know that the horizon area of a black hole will increase when it absorbs matters. While based on Barrow's idea of fractal black hole horizon, ones [Phys. Lett. B 831 (137181) 2022] had proposed that for a spherically fractal structure the minimal increase of the horizon area is the area of the smallest bubble sphere. And the corresponding black hole entropy is of a logarithmic form, which is similar to that of Boltzmann entropy under a certain condition. Based on these, we re-derive the entropy of the Barrow's Einstein-power-Yang-Mills (EPYM) AdS black hole, and calculate the temperature and heat capacity of the Barrow's EPYM AdS black hole. There exists an interesting phenomena that the ratio between the Barrow's temperature and the Hawking temperature of the EPYM AdS black hole is fully consistent with that of other Schwarzschild-like black holes. The Barrow's temperature and Hawking temperature with the certain range of $\Lambda$ are monotonically increasing and the corresponding heat capacities are all positive, which means these black holes are thermodynamically stable. Besides, for the Barrow's EPYM AdS black hole its heat capacity has a Schottky anomaly-like behavior, which may reflect the existence of the discrete energy level and the microscopical degree of freedom.