= Local radiative equilibrium
{title2=$\int\kappa_\nu(J_\nu-B_\nu)\,d\nu=0$}
A material element is in <local radiative equilibrium> when its absorbed and emitted radiative powers balance, so radiation causes no net local heating. In a non-scattering <grey atmosphere> in <local thermodynamic equilibrium>, this reduces to equality of the angular mean <specific intensity> $J$ and the <Planck function> $B$. Integrating the <radiative transfer equation> over <solid angle> then shows that the <radiative flux> is constant through a plane-parallel atmosphere. The radiation can remain anisotropic; equilibrium constrains its angular mean, not every ray separately.
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