Nonadiabatic charged spherical evolution in the postquasistatic approximation

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-Nordström 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.

11 pages, 16 Figures. Accepted for publication in Phys Rev D

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• Space-time inhomogeneity, anisotropy and gravitational collapse
• Relativistic gravitational collapse in comoving coordinates: The post-quasistatic approximation
• Electromagnetic effect on anisotropic scalar field collapse in higher curvature gravity
• On the equivalence of nonadiabatic fluids