# Exact black hole solutions with non-linear electrodynamic field

## TL;DR

This paper presents exact solutions for black holes in Einstein gravity coupled with nonlinear electrodynamics, revealing new properties influenced by the coupling constant, such as topological defects and varied horizon behaviors.

## Contribution

The study introduces novel exact black hole solutions with nonlinear electrodynamics, highlighting effects of the coupling constant absent in classical Einstein-Maxwell solutions.

## Key findings

- Presence of topological defects on the black hole horizon
- Electric charge can be much larger or smaller than mass depending on the coupling
- Event horizon radius approaches 2M for large coupling constant

## Abstract

We construct exact black hole solutions to Einstein gravity with nonlinear electrodynamic field. In these solutions, there are in general four parameters. They are physical mass, electric charge, cosmological constant and the coupling constant. Due to the presence of coupling constant, these solutions differ significantly from the Reissner-Nordstrom-de Sitter solution in Einstein-Maxwell gravity with a cosmological constant. In the first place, some of them are endowed with a topological defect on angle $\theta$. Secondly, for the extreme charged black holes, the electric charge can be much larger or much smaller than the mass by varying the coupling constant. Thirdly, for very large coupling constant, the radius of event horizon for some black holes approaches $2M$ regardless of the electric charge. Lastly, some black holes are asymptotically neither flat nor de Sitter (or anti-de Sitter).