# On the dynamical instability of self-gravitating systems

## TL;DR

This paper develops a generalized stability criterion for self-gravitating systems with anisotropy, extending the classical isotropic stability condition, and discusses its applications.

## Contribution

It introduces a new stability criterion based on the adiabatic local index that accounts for anisotropy in self-gravitating systems.

## Key findings

- The criterion generalizes the classical $<\gamma> \\geq 4/3$ stability condition.
- Applications demonstrate the criterion's usefulness in various scenarios.
- Provides insights into the stability behavior of anisotropic self-gravitating systems.

## Abstract

We study the dynamical stability of self-gravitating systems in presence of anisotropy. In particular, we introduce a stability criterion, in terms of the adiabatic local index, that generalizes the stability condition $<\gamma> \geq 4/3$ of the isotropic regime. Also, we discuss some applications of the criterion.