One of the important problems in Electromagnetics is the study of the equations of the electromagnetic field in various reference frames, hence in the Special and General Theory of Relativity, respectively. In a previous paper, we have developed tensor formulae in terms of the four-vector potential that allow one to express the electromagnetic field equations in polarized media (containing electrically and magnetically polarized substances) in good agreement with the International System of Units, whereas the widely known formulae correspond to non-polarized media and to the mixed Gauss system of units. The equations we have established refer to the Galilean system of reference. In the present paper, the equations will be extended to the case of any system of reference, using the covariant form of the equations. Certain proofs relative to covariant derivatives are also presented. The analysis developed in this paper is not found in any known work.

Keywords: Electromagnetic field equations, General theory of relativity.