# Black hole as a magnetic monopole within exponential nonlinear electrodynamics

## TL;DR

This paper explores magnetically charged black holes within an exponential nonlinear electrodynamics model, analyzing their solutions, thermodynamics, and phase transitions, revealing conditions for stability and critical phenomena.

## Contribution

It introduces a regular black hole solution in exponential nonlinear electrodynamics, including thermodynamic analysis and phase transition characterization.

## Key findings

- Derived the asymptotic black hole solution at infinity.
- Calculated the magnetic mass and metric function in terms of model parameters.
- Identified phase transition points via temperature sign change and heat capacity divergence.

## Abstract

We perform the gauge covariant quantization of the exponential model of nonlinear electrodynamics. Magnetically charged black holes, in the framework of our model are considered, and the regular black hole solution is obtained in general relativity. The asymptotic black hole solution at $r\rightarrow \infty$ is found. We calculate the magnetic mass of the black hole and the metric function which are expressed via the parameter $\beta$ of the model and the magnetic charge. The thermodynamic properties and thermal stability of regular black holes are analysed. We calculate the Hawking temperature of black holes and their heat capacity at the constant magnetic charge. We find a point where the temperature changes the sign that corresponds to the first-order phase transition. It is shown that at critical point, where the heat capacity diverges, there is a phase transition of the second-order. We obtain the parameters of the model when the black hole is stable.