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

Abstract

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.

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.…”