Lower bound on the radii of circular orbits in the extremal Kerr black-hole spacetime

It is often stated in the physics literature that maximally-spinning Kerr black-hole spacetimes are characterized by near-horizon co-rotating circular geodesics of radius $r_{\text{circular}}$ with the property $r_{\text{circular}}\to r_{\text{H}}^{+}$, where $r_{\text{H}}$ is the horizon radius of the extremal black hole. Based on the famous Thorne hoop conjecture, in the present compact paper we provide evidence for the existence of a non-trivial lower bound $\frac{r_{\text{circular}-r_{\text{H}}}}{r_{\text{H}}}\gtrsim (\mu \mathrm{/}M{)}^{1\mathrm{/}2}$ on the radii of circular orbits in the extremal Kerr black-hole spacetime, where $\mu \mathrm{/}M$ is the dimensionless mass ratio which characterizes the composed black-hole-orbiting-particle system.