Electric field in 3D gravity with torsion

TL;DR

This paper explores the behavior of electric fields in three-dimensional gravity with torsion, revealing constraints on Maxwell components and presenting an exact solution influenced by spacetime's asymptotic structure.

Contribution

It provides the first exact solution for azimuthal electric fields in 3D gravity with torsion, highlighting the role of central charges in the geometric structure.

Findings

At least one Maxwell component must vanish in static, spherically symmetric configurations.

An exact azimuthal electric field solution is derived.

The solution's geometry depends on two central charges related to AdS asymptotics.

Abstract

It is shown that in static and spherically symmetric configurations of the system of Maxwell field coupled to 3D gravity with torsion, at least one of the Maxwell field components has to vanish. Restricting our attention to the electric sector of the theory, we find an interesting exact solution, corresponding to the azimuthal electric field. Its geometric structure is to a large extent influenced by the values of two different central charges, associated to the asymptotic AdS structure of spacetime.