  No positive result has been obtained on the magnetic monopoles search. This
allows to consider different theoretical approaches as the proposed in this
paper, developed in the framework of the Einstein General Relativity. The
properties of second rank skew-symmetrical fields are the basis of
electromagnetic theories. In the space-time the Hodge duality of these fields
is narrowly related with the rotations in the SO(2) group. An axiomatic
approach to a dual electromagnetic theory is presented. The main result of this
paper is that the stress-energy tensor can be decomposed on two parts: the
parallel and the perpendicular. The parallel part is easily integrated on the
Lagrangian approach, while some problems appears with the perpendicular part. A
solution with the parallel part alone is found, it generates a non-standard
model of magnetic monopoles neutral to the electric charges.
