Stationary radiation density
= Stationary radiation density
{title2=$\rho N^4=C$}
The <equation of state> of isotropic <blackbody radiation> is $p=\rho/3$. The <barotropic hydrostatic first integral> gives $\rho N^4=C$. The <Stefan–Boltzmann law> $\rho\propto T^4$ then yields the <Tolman–Ehrenfest relation> $TN=\mathrm{constant}$. Here $N=\sqrt{|K^aK_a|}$ for the stationary timelike <Killing vector field>; its normalization only changes the constants.