Transport processes in the gravitational collapse of an anisotropic fluid

In this paper we introduce a method to study the influence of thermal conduction and viscous processes in a spherically symmetric gravitational collapse. We assume that the viscosity appears because of the interaction between the neutrinos and the matter that composes the fluid. The temperature, bulk viscous pressure, and shear viscous pressure are found. The effect of the latter in the anisotropy of the fluid is studied as well. To this end it is necessary to solve two sets of partial differential equations. First, the Einstein equations are solved using the seminumerical HJR method. The causal Maxwell-Cattaneo-type transport equations form the second set of equations to be solved. The temperature profile, found from the heat transport equation, indicates that the energy of the neutrinos in the surface is not correlated with that of the interior. This behavior, which can be explained in terms of the Eddington approximation, allows us to estimate the thickness of the neutrinosphere. The contribution of the shear viscous pressure to the anisotropy in the core of the star is found to be non-negligible.