= Radiative-equilibrium obstruction in a rotating barotropic star
{title2=$\nabla\cdot(f\nabla\phi)=f'|\nabla\phi|^2+f\nabla^2\phi$}
= von Zeipel paradox
{c}
{synonym}
On a regular <equipotential surface>, $f,f',\rho$ and $\nabla^2\phi$ are constant, but $|\nabla\phi|^2$ generally varies. Consequently a flux $\mathbf F=f(\phi)\nabla\phi$ cannot ordinarily satisfy local <radiative equilibrium> $\nabla\cdot\mathbf F=\rho\epsilon$ at all latitudes. Special cases such as $f'=0$ or spherical symmetry evade this obstruction. <Stellar meridional circulation> supplies heat advection in the leading hydrostatic treatment.
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