Radial stellar pulsation equation
= Radial stellar pulsation equation
{title2=$\xi_r=r\eta$}
For a radial <stellar oscillation>, put $\xi_r=r\eta$. The self-gravitating adiabatic equation is $(\Gamma_1Pr^4\eta^{\prime})^{\prime}+r^3[(3\Gamma_1-4)P]^{\prime}\eta+\rho r^4\omega^2\eta=0$. It is a <Sturm-Liouville problem> whose <Rayleigh quotient> tests radial stability. The familiar constant-exponent threshold is $\Gamma_1=4/3$; a variable exponent requires the full integral test.