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

Abstract

The authors present a treatment of classical electromagnetic theory in the presence of a weak gravitational field, both in a vacuum and in a material medium, in terms of an effective dielectric and magnetic permeability tensor. They show 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. They derive the dispersion relation for an electromagnetic wave in a medium and show that it depends upon the polarisation state of light.