Some consequences of the Einstein covariance principle in electrodynamics of media

We show that the Einstein covariance principle provides an opportunity to generate infinitely many solutions of given covariant equation from a known one. With use of this statement we derive exact expressions for charge and current densities in a medium in an arbitrary external field. We obtain that in a homogeneous nondispersive medium the field of a point particle differs at short-distances from the well known expression. We also demonstrate that in a linear medium second harmonic generation and optical detection become possible in the field of radially polarized radiation.