= Barotropic relativistic sound speed
{title2=$c_s^2=dp/d\rho$}
In units $c=1$, an isentropic <perfect fluid in general relativity> has sound speed $c_s^2=dp/d\rho$. Writing $n=p'(\epsilon)$ gives $d\rho=\epsilon\,dn$ and $c_s^2=n/(\epsilon p''(\epsilon))$. Linearized <particle number conservation in a relativistic fluid> and the <relativistic Euler equation> then yield acoustic waves with this speed. Positive $c_s^2$ is needed for ordinary acoustic stability; a causal fluid model additionally requires $c_s^2\le1$.
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