= Equatorial circular Kerr photon orbit
{title2=$r^2-3Mr\pm2a\sqrt{Mr}=0$}
For $0<a<M$, the two exterior equatorial <circular null geodesics> of the <Kerr metric> have radii solving the signed equation above. The plus sign gives the prograde branch and the minus sign gives the retrograde branch. To derive it put $b=L/E$ in the double-root conditions of the <equatorial Kerr null geodesic radial equation>: $r^2=(b^2-a^2)/3$ and $r^3=M(b-a)^2$. Both exterior radii exceed $r_+=M+\sqrt{M^2-a^2}$ and approach $3M$ when $a\to0$. The horizon generators are a separate case with $E=L=0$; dividing by $E$ excludes them. Constant-radius null directions at other exterior radii generally have nonzero acceleration and are not <geodesics>.
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