# Thermodynamics of the Bardeen Black Hole in Anti-de Sitter Space

## TL;DR

This paper investigates the thermodynamics and phase transitions of Bardeen-AdS black holes, revealing a critical magnetic monopole parameter and analyzing stability through heat capacity and Gibbs free energy.

## Contribution

It provides a detailed thermodynamic analysis of Bardeen-AdS black holes, including the identification of a critical magnetic charge and stability criteria.

## Key findings

- Identified the minimal stable radius of the black hole.
- Discovered a critical magnetic charge value $g_m$ affecting phase transitions.
- Analyzed thermodynamic stability using heat capacity and Gibbs free energy.

## Abstract

We first study the thermodynamics of Bardeen-AdS black hole by the $T$-$r_{h}$ diagram, where T is the Hawking temperature and $r_{h}$ is the radius of event horizon. The cut-off radius which is the minimal radius of the thermodynamical stable Bardeen black hole can be got, and the cut-off radius is the same with the result of the heat capacity analysis. Moreover, by studying the parameter $g$, which is interpreted as a gravitationally collapsed magnetic monopole arising in a specific form of non-linear electrodynamics, in the Bardeen black hole, we can get a critical value $g_{m}$ and different phenomenons with different values of parameter $g$. For $g>g_{m}$, there is no second order phase transition. We also research the thermodynamical stability of the Bardeen black hole by the Gibbs free energy and the heat capacity. In addition, the phase transition is discussed.