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

Shahar Hod

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arXiv · 2502.12244

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

Shahar Hod

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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 $r_{\text{circular}}\to r^+_{\text{H}}$, 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 ${{r_{\text{circular}}-r_{\text{H}}}\over{r_{\text{H}}}}\gtrsim (\mu/M)^{1/2}$ 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.

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Shahar Hod. 2025-02-17. Lower bound on the radii of circular orbits in the extremal Kerr black-hole spacetime. https://arxiv.org/abs/2502.12244

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