# 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.

## Key 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 $\zo$.