In this work, a generalized framework of the post-quasistatic approximation in higher dimensional non-comoving coordinates is presented. We study the evolution of adiabatically radiating and dissipative fluid configuration in higher dimensional post-quasi-static approximation. An iterative method for describing self-gravitating spheres is developed for this purpose. Dissipation is described by free-streaming radiation and heat flux. We match the higher dimensional interior solution, in non-comoving coordinates, with the corresponding Vaidya exterior solution. The generalized form of post-quasistatic approximation leads to a system of higher dimensional surface equations. The surface equations are of significant importance in the understanding of the physical phenomenon like luminosity, Doppler shift and red-shift at the boundary surface of gravitating sources.

The development of dissipative and electrically charged distributions in five dimensions is presented by using the post-quasistatic approximation. It is an iterative technique for the evolution of self-gravitating spheres of matter. We construct non-adiabatic distributions by means of an equation of state that accounts for the anisotropy based on electric charge. Streaming out and diffusion approximations are used to describe dissipation. In non-comoving coordinates, we match the higher dimensional interior solution with the corresponding Vaidya–Reissner–Nordström exterior solution. Hence, a system of higher dimensional surface equations results from generalized form of the post-quasistatic approximation. Surface equations are essential for understanding physical phenomena such as luminosity, Doppler shift, and red-shift at the boundary surface of gravitating sources.