Divergence of Electric Field of Continuous and of a Point Charge for   Relativistic and non-Relativistic Motion
  In this paper we considered divergence of electric and of magnetic fields for four cases: classical point charge, classical continuous charge, relativistic point and relativistic continuous charges. Results for classical and relativistic point charges are the same as in literature, i.e. Gauss's law is valid. However results for time-varying classical and relativistic distributed charges indicate that divergence of electric field is not zero even for volumes of space where no charges are present. For these cases original Gauss's law might require modification. Divergence of electric field seems to be far-field type scalar anisotropic field, which is generated by time-varying electric charges or currents. Results indicate that for these effects to be sufficiently large to be experimentally observable the time variation of electric charges and/or of currents should be very fast. Divergence of magnetic field is zero for all cases. 
Altay Zhakatayev
physics.class-ph