Gravitational Instability in Presence of Bulk Viscosity: the Jeans Mass and the Quasi-Isotropic Solution

TL;DR

This paper investigates how bulk viscosity affects gravitational instability and structure formation, analyzing both Newtonian and relativistic regimes, and finds viscosity dampens perturbations but does not alter the Jeans mass.

Contribution

It introduces a combined analysis of gravitational instability with bulk viscosity in both Newtonian and relativistic frameworks, highlighting the damping effects and conditions for solutions.

Findings

Viscosity dampens perturbation growth in Newtonian regime.

Jeans mass remains unchanged despite viscosity effects.

Relativistic solutions exist only within specific parameter domains.

Abstract

This paper focuses on the analysis of the gravitational instability in presence of bulk viscosity both in Newtonian regime and in the fully-relativistic approach. The standard Jeans Mechanism and the Quasi-Isotropic Solution are treated expressing the bulk-viscosity coefficient $\zeta$ as a power-law of the fluid energy density $\rho$, i.e., $\zeta=\zo\rho^{s}$. In the Newtonian regime, the perturbation evolution is founded to be damped by viscosity and the top-down mechanism of structure fragmentation is suppressed. The value of the Jeans Mass remains unchanged also in presence of viscosity. In the relativistic approach, we get a power-law solution existing only in correspondence to a restricted domain of $\zo$.