An extension of teleparallelism and the geometrization of the electromagnetic field

As is well known, both Weyl and Weitzenböck spacetimes were initially used as attempts to geometrize the electromagnetic field. In this paper, we prove that this field can also be regarded as a geometrical quantity in an extended version of the Weitzenböck spacetime. The new geometry encompasses features of both Weyl and Weitzenböck 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.