How does spin orientation affect the ISCO around a rotating black hole?

• A. Prograde orbits place the ISCO closer to the horizon; retrograde orbits place it farther out.
• B. Prograde orbits place the ISCO farther out; retrograde closer.
• C. Spin orientation has no effect on the ISCO.
• D. The ISCO radius is always located at the event horizon.

Answer: (A)

The effect being tested is how a black hole’s spin and the direction of the orbit change the radius of the innermost stable circular orbit (ISCO) through frame dragging. In a rotating (Kerr) black hole, spacetime itself is dragged around the spin axis. If a particle orbits in the same direction as the spin (prograde), this dragging helps the particle stay in a stable orbit at smaller radii, so the ISCO moves inward toward the horizon. If the orbit is opposite to the spin (retrograde), the dragging works against the motion, requiring a larger radius for stability, so the ISCO moves outward. This is why prograde orbits have ISCOs closer to the horizon, while retrograde orbits have ISCOs farther out. The Schwarzschild case without spin sits at an ISCO of 6M, showing how spin orientation shifts the radius from that baseline in opposite directions depending on prograde vs retrograde.