5.1. Gravitational Instability

The most viable framework for the formation of galaxies is still that of a self-gravitating fluid which experiences a critical instability. There are three basic equations from classical physics that govern the behavior of this self-gravitating fluid. We assume the fluid to be neutral and non-turbulent. In reality, the role of magnetic fields and turbulence, as it relates to galaxy formation, is completely unknown but may be pivotal. Unfortunately we lack the framework for incorporating these effects. The three basic equations we consider in identifying the process of gravitational instability and galaxy formation are, the equation of continuity, Euler's equation and Poisson's equation. These set the foundation for linear perturbation theory as first applied by Jeans to define various criterion against which the fluid is unstable to collapse.