= Radiation fluid has no regular free surface
{title2=$\rho=C/N^4>0$}
A connected nonvacuum <perfect fluid> with <equation of state> $p=\rho/3$ obeys the <stationary radiation density> law $\rho=C/N^4$ with $C>0$. On a compact region of a regular <spacetime>, a smooth <Killing vector field> has bounded norm. Consequently $\rho$ cannot tend to zero at a finite regular <free surface>. A vanishing timelike norm instead makes the density diverge. A radiation-filled cavity can have a material wall with nonzero boundary <pressure>; this is a different boundary condition.
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