Shear viscosity in the postquasistatic approximation

Abstract

We apply the postquasistatic approximation, an iterative method for the evolution of selfgravitating spheres of matter, to study the evolution of anisotropic non-adiabatic radiating and dissipative distributions in General Relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in non-comoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity. PACS numbers: 04.25.-g,04.25.D-,0.40.-b

Structure Scalars in Charged Plane Symmetry

“…Moreover, they formulated a relationship between the Weyl tensor and energy-density inhomogeneity. Rosales et al [10] pointed out that electric charge plays the same role of anisotropy in the collapse [11], when the tangential pressure is greater than radial pressure.…”

Heat flow in the postquasistatic approximation

“…In this paper we considered heat flow as a transport mechanism in the PQSA. Heat flow produces a stable configuration, which is the opposite effect of viscosity [4]. This result indicates that a combination of viscosity (anisotropy) with heat flow may be crucial for gravitational collapse or at least just out of equilibrium, where we expect the PQSA is a good approach.…”

Nonadiabatic charged spherical evolution in the postquasistatic approximation

“…The system clearly departs equilibrium and collapses. Electric charge contributes to the collapse in the same way that anisotropy with tangential pressure greater than radial pressure favors the collapse [73], irrespective of the transport mechanism. In any case electric charge has to be huge to change the fate of the gravitational collapse.…”

“…We considered the dissipation by viscosity and heat flow separately [73], [80], in order to isolate similar effects with different mechanisms. In this work we considered heat flow/streaming out and anisotropy induced by electric charge, pointing to the most realistic numerical modeling in this area [35].…”

“…In Sec. II we write the field equations for Bondian observers to show how the electric charge induces anisotropy, matching with the exterior Reissner-Nordström-Vaidya solution, and write the surface equation, following the PQSA protocol [15], [73]. In Sec.…”