= Equatorial Kerr null geodesic radial equation
{title2=$r^4\dot r^2=[E(r^2+a^2)-aL]^2-\Delta(L-aE)^2$}
For an equatorial <null geodesic> of the <Kerr metric>, $E=-p_t$ and $L=p_\phi$ are <geodesic conserved quantities from Killing vectors>. In units $G=c=1$, $\Delta=r^2-2Mr+a^2$, and an <affine parameter> gives the displayed equation. It follows by solving the stationary and axial momentum equations for $\dot t,\dot\phi$ and substituting them into the <null condition>. A zero of its radial polynomial is only a turning point; an exterior <circular null geodesic> also requires the derivative of that polynomial to vanish with $E,L$ held fixed.
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