= Radiative gradient in a uniformly rotating star
{title2=$\nabla_{\rm rad}=\frac{3\kappa PL}{16\pi acGmT^4}\left(1-\frac{\Omega^2V}{2\pi Gm}\right)^{-1}$}
The <divergence theorem> and <Poisson equation> give $\int_S\nabla\phi\cdot d\mathbf S=4\pi Gm-2\Omega^2V$ on a bounding <equipotential surface>. <Equipotential luminosity conservation with stellar circulation> then fixes $f=L/(4\pi Gm-2\Omega^2V)$. Combining $dT/d\phi=-f/\chi$, $dP/d\phi=-\rho$ and <radiative conductivity> gives the displayed logarithmic temperature-pressure gradient. Both appearances of mass mean the enclosed mass $m$; only on the outer boundary can both be replaced by the total mass.
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