On the relativistic theory of electromagnetic dispersion relations and Poynting's theorem

Constitutive relations, and general dispersion relations, are derived for an arbitrary, anisotropic, dispersive and dissipative medium which is moving relative to an inertial observer. The constitutive relations are expressed in terms of the ''local'' dielectric tensor, magnetic permeability, etc., where ''local'' refers to the instantaneous rest frame of the medium. We also give the generalization of Poynting's theorem for power flow including the expression for the rate at which the moving medium does work on the radiation. In view of the current interest in radiation generated in, and passing through, pulsar magnetospheres, we believe that the general results presented here are, perhaps, not without some astrophysical import