Nonadiabatic charged spherical evolution in the postquasistatic approximation

TL;DR

This paper studies the evolution of charged, dissipative spherical matter distributions in General Relativity using the postquasistatic approximation, revealing how different dissipation mechanisms influence collapse dynamics and charge distribution.

Contribution

It introduces an application of the postquasistatic approximation to charged, dissipative spheres, comparing diffusion and streaming out models in gravitational collapse.

Findings

Diffusion stabilizes collapse, forming a short-lived spherical shell.

Streaming out radiation efficiently emits energy and redistributes charge.

Collapse behavior varies significantly between diffusion and streaming out models.

Abstract

We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of dissipative and electrically charged distributions in General Relativity. We evolve nonadiabatic distributions assuming an equation of state that accounts for the anisotropy induced by the electric charge. Dissipation is described by streaming out or diffusion approximations. We match the interior solution, in noncomoving coordinates, with the Vaidya-Reissner-Nordstr\"om exterior solution. Two models are considered: i) a Schwarzschild-like shell in the diffusion limit; ii) a Schwarzschild-like interior in the free streaming limit. These toy models tell us something about the nature of the dissipative and electrically charged collapse. Diffusion stabilizes the gravitational collapse producing a spherical shell whose contraction is halted in a short characteristic hydrodynamic time. The streaming out radiation provides a more efficient mechanism for emission of energy, redistributing the electric charge on the whole sphere, while the distribution collapses indefinitely with a longer hydrodynamic time scale.