An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self–gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post–quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce
the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition.
As a special feature of the model , we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure.