# Three dimensional magnetic solutions in massive gravity with (non)linear field

## TL;DR

This paper explores three-dimensional magnetic solutions in massive gravity with nonlinear electromagnetic fields, analyzing their geometrical properties, phase transitions, and differences between de Sitter and anti-de Sitter spacetimes.

## Contribution

It introduces novel magnetic solutions in massive gravity with nonlinear fields and examines their geometrical and phase transition properties.

## Key findings

- Differences between de Sitter and anti-de Sitter solutions are identified.
- Conditions for phase transitions in the solutions are established.
- Effects of massive gravity and nonlinear fields on solution properties are analyzed.

## Abstract

The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings) in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.