Dielectric tensor and magnetic permeability in the weak field approximation of general relativity

A treatment of classical electromagnetic theory in the presence of a weak gravitational field, both in a vacuum and in a material medium is presented in terms of an effective dielectric and magnetic permeability tensor. It is shown that the gravitational red shift can be interpreted as the work done by the electric field of the light ray against the gravitationally induced polarisation current. The dispersion relation for an electromagnetic wave in a medium is derived and it is shown that it depends upon the polarisation state of light. (author)