In a previous work some of the authors have solved the Einstein equations of General Relativity for a class of metrics with constant spatial curvature, where it was found a non vanishing Weyl tensor in the presence of an energy-momentum tensor with an anisotropic pressure component. Here, we perform the perturbative analysis of this model in order to study the gravitational stability under linear scalar perturbations. For this purpose, we take the Quasi-Maxwellian formalism of General Relativity as our framework, which offers a naturally covariant and gauge-invariant approach to deal with perturbations that are directly linked to observational quantities. We also consider a generalization of the causal thermodynamics to include the effect of the non-null Weyl tensor, which introduces a “viscosity” due solely to gravitational tidal forces.
Date added: Fri, 18 Oct 13