Some consequences of the Einstein covariance principle in electrodynamics of media

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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.