= Uniformly rotating gas-sheet dispersion relation
{title2=$\omega^2=c^2k^2-2\pi G\Sigma_0|k|+4\Omega^2$}
For a homogeneous inviscid <razor-thin disk approximation> with <solid-body rotation> and barotropic <sound speed> $c$, the compressive wave branch obeys $\omega^2=c^2k^2-2\pi G\Sigma_0|k|+4\Omega^2$. The <razor-thin disk Poisson kernel> supplies the <self-gravity> term, and the <radial epicyclic frequency> is $2|\Omega|$. Growing modes have $\omega^2<0$; a separate zero-frequency balanced mode can also exist.
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