Analysis of heat flow in the post-quasi-static approximation for gravitational collapse in five dimension

Abstract

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.

Five dimensional analysis of electromagnetism with heat flow in the post-quasi-static approximation

“…More precisely, the authors [61] employed a method for modeling the evolution of compact objects that does not necessitate complete integration of the EFEs with respect to the time coordinate. Zahra et al presented the general framework of the PQS approximation with heat flow in five dimensional noncomoving coordinates [66].…”

The Post-Quasi-Static Approximation: An Analytical Approach to Gravitational Collapse

“…Between the two aforementioned approaches, we have seminumerical techniques, which may be regarded as a "compromise" between the analytical and numerical approaches. These techniques are based on the PQSR approximation mentioned above, and were developed in [7][8][9][10] (see also [36,37]). This third approach allows to reduce the initial system of partial differential equations into a system of ordinary differential equations (referred to as surface equations) for quantities evaluated at the boundary surface of the fluid distribution.…”

“…• Assuming a specific luminosity profile obtained from observations and using (36) or (37), we obtain a relationship between the two arbitrary functions of t mentioned above, thereby reducing (33) to an ordinary differential equation for one variable.…”