Covariance of Maxwell equations and comparison of electrodynamic systems

As is well known, Maxwell equations in vacuum are covariant under a transformation of the Lorentz group. The same equations in a material medium have a more general symmetry group and retain their form under arbitrary nondegenerate linear transformations of space-time variables to which, naturally, are added definite rules for recalculating fields and material characteristics of the medium. This enables a formal correspondence to be established between solutions of physically different electrodynamic problems related by linear transformations of the space-metric and of the tensor characteristics of the media. Such a correspondence (comparison) turns out to be useful, in particular, for investigating the propagation of electromagnetic waves in the presence of external gravitational fields, and also in systems with moving inhomogeneities or sources. Some examples of comparisons are examined and the results obtained in the course of this are indicated. A discussion is given of the relationship of the comparison method to the transformations of special and general theories of relativity.