 Gravitational instability

Gravitational instability is the growth of a perturbation because its increased self-gravity overcomes the opposing support or restoring response. For a uniform nonexpanding gas, linearization gives the Jeans instability dispersion relation ${\omega }^2=c_s^2{k}^2-4\pi G\rho$: sufficiently long wavelengths grow rather than oscillate. In an expanding universe the background and Hubble friction modify the growth rate; a pressureless growing density mode can eventually become nonlinear. Rotation, magnetic stress, pressure and geometry can all alter the stability threshold in other systems.

Gravitational instability refers to a situation in which a cloud of gas, dust, or other matter becomes susceptible to gravitational collapse due to its own weight, leading to the formation of denser regions. This concept is crucial in astrophysics and cosmology, particularly in the context of star formation and the large-scale structure of the universe.