
TL;DR
This paper investigates the behavior of the innermost stable circular orbit (ISCO) and photon orbit in extremal Kerr black holes, revealing their different properties on various spacetime slices and their relation to the horizon.
Contribution
It clarifies the geometric relationship between the ISCO, photon orbit, and horizon in extremal Kerr black holes across different spacetime slices.
Findings
ISCO and photon orbit differ from the horizon on constant time slices.
On horizon-crossing slices, ISCO and photon orbit coincide with the horizon generators.
The study enhances understanding of extremal Kerr black hole geometry.
Abstract
Although the circular photon orbit and ISCO for the Kerr black hole remain distinct from each other and from the horizon in the extremal spin limit on a constant Boyer-Lindquist time slice, on a horizon-crossing slice they both coincide with the null generators of the horizon.
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