Nonlinear electrodynamics in 3D gravity with torsion

TL;DR

This paper explores exact solutions in three-dimensional gravity with torsion coupled to nonlinear electrodynamics, revealing constraints on electromagnetic fields and discovering novel self-dual solutions with topological modifications.

Contribution

It provides the first exact solutions in 3D gravity with torsion coupled to nonlinear electrodynamics, including self-dual solutions with topological mass terms.

Findings

At least one electromagnetic component vanishes in static, spherically symmetric configurations.

An exact solution with azimuthal electric field is constructed.

Two types of self-dual solutions are found when a topological mass term is included.

Abstract

We study exact solutions of nonlinear electrodynamics coupled to three-dimensional gravity with torsion. We show that in any static and spherically symmetric configuration, at least one component of the electromagnetic field has to vanish. In the electric sector of the theory, we construct an exact solution, characterized by the azimuthal electric field. When the electromagnetic action is modified by a topological mass term, we find two types of the self-dual solutions.