Stability Analysis of a Self-Gravitating Fluid within EIT Theory

In this article, we apply the formalism of (classical) Extended Irreversible Thermodynamics (EIT) to the dynamics of density fluctuations for a self-gravitating fluid in a static Universe, considering only bulk viscosity. The problem is characterized by gravitational instability, for which the Jeans criterion is shown to hold. However, both the relaxation time in the constitutive equation and the viscosity itself affect the behavior of both stable and unstable modes. In particular, the stable scenario features three modes, two of them corresponding to damped oscillations which decay faster that in the CIT scene. The third mode, inexistent in the CIT, corresponds to a very quickly decaying mode. In the unstable case, growing modes are observed in both EIT and CIT theories, for which the slowest growth is the one predicted by the CIT theory followed by the EIT, while the non-dissipative case corresponds to the fastest one.