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An evolution of radiant shock wave front is considered in the framework of arecently presented method to study self-gravitating relativistic spheres, whoserationale becomes intelligible and finds full justification within the contextof a suitable definition of the post-quasistatic approximation. The sphericalmatter configuration is divided into two regions by the shock and each side ofthe interface having a different equation of state and anisotropic phase. Inorder to simulate dissipation effects due to the transfer of photons and/orneutrinos within the matter configuration, we introduce the flux factor, thevariable Eddington factor and a closure relation between them. As we expectedthe strength of the shock increases the speed of the fluid to relativisticvalues and for some critical ones is larger than light speed. In addition, wefind that energy conditions are very sensible to the anisotropy, specially thestrong one. As a special feature of the model, we find that the contribution ofthe matter and radiation to the radial pressure are the same order of magnitudeas in the mant as in the core, moreover, in the core radiation pressure islarger than matter pressure.Comment: To appear in Journal of Physics:Conference Series:"XXIX Spanish  Relativity Meeting (ERE 2006): Einstein's Legacy: From the Theoretical  Paradise to Astrophysical Observations

General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation