 Kerr ISCO efficiency limits

For ideal zero-torque equatorial thin discs, efficiency is $1-E_{\mathrm{ISCO}}$. The formal extremal retrograde, Schwarzschild and extremal prograde limiting radii are respectively $9,6,1$ in units $GM/c^2$, giving efficiencies $1-\sqrt{25/27}$, $1-\sqrt{8/9}$ and $1-1/\sqrt{3}$. Photon capture and non-ideal accretion can change the realized efficiency.