Higher-dimensional compact objects with radiative viscous flow

In this paper, we develop a set of equations and associated matching conditions that are essential for the dissipation process in spherical symmetry. This process is characterized by both viscosity and free-streaming radiation, which are approximated using both free-streaming and diffusion methods. Our study focuses on a spherical distribution of matter that contains a fluid that dissipates. By using non-comoving coordinates with the post-quasi-static (PQS) approximation, we are able to analyze viscous fluid spheres as they depart from equilibrium in the streaming-out limit. In this work, we study a technique for obtaining a PQS approximation of the algorithm in non-comoving coordinates, which are used to discuss the phenomenon of gravitational collapse (GC). The PQS approximation is a step-by-step algorithm for evolving self-gravitating matter spheres. The system of surface equations is developed by matching the inner spacetime with the Vaidya outer spacetime. These surface equations play a crucial role in the study of various physical phenomena, including luminosity, redshift, and Doppler shift at gravitational source boundary surfaces (BS).