# Magnetically charged black hole in framework of nonlinear electrodynamics model

## TL;DR

This paper introduces a nonlinear electrodynamics model that produces regular magnetic black hole solutions with unique horizon structures and thermodynamic properties, including phase transitions and stability conditions.

## Contribution

The study presents a novel nonlinear electrodynamics framework yielding regular magnetic black holes with detailed thermodynamic analysis and phase transition insights.

## Key findings

- Regular magnetic black hole solutions with corrected Reissner-Nordström metrics
- Existence of one, two, or no horizons depending on parameters
- Identification of second-order phase transitions and stability regions

## Abstract

A model of nonlinear electrodynamics is proposed and investigated in general relativity. We consider the magnetic black hole and find a regular solution which gives corrections into the Reissner-Nordstr\"{o}m solution. At $r\rightarrow\infty$ the asymptotic spacetime becomes flat. The magnetic mass of the black hole is calculated and the metric function is obtained. At some values of the model parameter there can be one, two or no horizons. Thermodynamics of black holes is studied and we calculate the Hawking temperature and heat capacity of black holes. It is demonstrated that there is a phase transition of second order. At some parameters of the model black holes are thermodynamically stable.