Jean’s Instability
Jeans (1902) tackled gravitational instability in
a static medium, dR/dt = 0 in eq. 11.24 we can
get the dispersion relation for waves of the
form ∆=∆0 exp i (k∙r – ωt):
This relation describes oscillations or instability depending on the
sign of the right hand side.  If positive, oscillatory as pressure
gradient supports the region for wavelengths less than the critical
Jean’s wavelength: