= Linear adiabatic stellar oscillation equations
{title2=$\Delta P/P=\Gamma_1\Delta\rho/\rho$}
For a static spherical star, a <fluid displacement> $\boldsymbol\xi e^{-i\omega t}$ gives $\rho_1=-\nabla\cdot(\rho\boldsymbol\xi)$, $-\omega^2\rho\boldsymbol\xi=-\nabla p_1-\rho_1\nabla\Phi-\rho\nabla\phi_1$ and $\nabla^2\phi_1=4\pi G\rho_1$. The adiabatic relation is $\Delta P=-\Gamma_1P\nabla\cdot\boldsymbol\xi$. Centre regularity and surface mechanical/gravitational boundary conditions select discrete <eigenvalues> in a conservative model.
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