Torsion and the Electromagnetic Field

TL;DR

This paper explores how electromagnetic fields interact with torsion in teleparallel gravity, showing they can both couple to and generate torsion while maintaining gauge invariance.

Contribution

It demonstrates the bidirectional coupling between electromagnetic fields and torsion within teleparallel gravity, preserving gauge invariance.

Findings

Electromagnetic fields can produce torsion through their energy-momentum tensor.

Electromagnetic coupling to torsion does not break gauge invariance.

Electromagnetic fields can both couple to and generate torsion in this framework.

Abstract

In the framework of the teleparallel equivalent of general relativity, we study the dynamics of a gravitationally coupled electromagnetic field. It is shown that the electromagnetic field is able not only to couple to torsion, but also, through its energy-momentum tensor, to produce torsion. Furthermore, it is shown that the coupling of the electromagnetic field with torsion preserves the local gauge invariance of Maxwell's theory.