An Extension of Teleparallelism and the Geometrization of the Electromagnetic Field

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.