An Extension of Teleparallelism and the Geometrization of the Electromagnetic Field

TL;DR

This paper introduces an extended geometry combining Weyl and Weitzenb"ock features, enabling the electromagnetic field to be described geometrically and deriving Einstein-Maxwell equations from a purely geometric action.

Contribution

It presents a novel extended geometry that unifies aspects of Weyl and Weitzenb"ock spacetimes, allowing a purely geometric formulation of electromagnetism and Einstein-Maxwell equations.

Findings

Electromagnetic field can be geometrized in the extended Weitzenb"ock spacetime.

Derived Einstein's equations coupled with Maxwell energy-momentum tensor from geometric action.

Constructed a conformal invariant teleparallel model using the new geometry.

Abstract

As is well known, both Weyl and Weitzenb\"ock spacetimes were initially used as attempts to geometrize the electromagnetic field. In this letter, we prove that this field can also be regarded as a geometrical quantity in an extended version of the Weitzenb\"ock spacetime. The new geometry encompasses features of both Weyl and Weitzenb\"ock spacetimes. In addition, we obtain Einstein's field equations coupled to the Maxwell energy-momentum tensor from a purely geometrical action and, to exemplify the advantage of using this new geometry when dealing with conformal invariance, we construct a model that is equivalent to a known conformal invariant teleparallel model.