Maxwell electrodynamics in media, geometry effects on constitutive relations

The problems of constitutive relations in Maxwell electrodynamics, their possible form, its behavior under the motion of the reference frame, its connection with Special Relativity theory, interplay between constitutive relations and gravity are reviewed. The main accent in our treatment is the known possibility to simulate material media by geometrical methods. These problems have a long history. We can track interest to the problem in the huge literature that has been produced on this issue. Note that Gordon was first seemed largely interested in trying to describe dielectric media by an effective metrics; Gordon tried to use a gravitational field to mimic a dielectric medium. The idea was taken up and developed by Tamm and Mandel’stam