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

Abstract

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}}rightarrow 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 {{r_{text {circular}}-r_{text {H}}}over {r_{text {H}}}}gtrsim (mu /M)^{1/2} on the radii of circular orbits in the extremal Kerr black-hole spacetime, where mu /M is the dimensionless mass ratio which characterizes the composed black-hole-orbiting-particle system.