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

Abstract

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 $$r_{\text {circular}}$$ rcircular with the property $$r_{\text {circular}}\rightarrow r^+_{\text {H}}$$ rcircular→rH+ , where $$r_{\text {H}}$$ rH 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 $${{r_{\text {circular}}-r_{\text {H}}}\over {r_{\text {H}}}}\gtrsim (\mu /M)^{1/2}$$ rcircular-rHrH≳(μ/M)1/2 on the radii of circular orbits in the extremal Kerr black-hole spacetime, where $$\mu /M$$ μ/M is the dimensionless mass ratio which characterizes the composed black-hole-orbiting-particle system.