Innermost Stable Circular Orbit

The Innermost stable circular orbit (often called the ISCO) is the smallest orbit in which a test particle can stably orbit a massive object in general relativity. The location of the ISCO, the ISCO-radius (${\displaystyle r_{isco}}$), depends on the angular momentum (spin) of the central object.

For a non-spinning massive object, where the gravitational field can be expressed with the Schwarzschild metric, the ISCO is located at,

As the angular momentum of the central object increases, ${\displaystyle r_{isco}}$ decreases. Even for a non-spinning object, the ISCO radius is only three times the Schwarzschild radius, suggesting that only black holes have innermost stable circular orbits outside of their surfaces.

For a photon, the circular orbit occurs at

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