The innermost stable circular orbit is the smallest stable circular timelike orbit around a black hole. Its radius and orbital energy depend on black-hole spin and on whether the orbit is prograde or retrograde.
For equatorial test-particle circular orbits in the extremal-spin limit, the prograde Kerr black hole innermost stable circular orbit has Boyer-Lindquist radius tending to and specific energy tending to . The retrograde limit has radius and specific energy . The prograde radius approaching the horizon coordinate does not make the massive limiting orbit identical to the null horizon generator.[ref]
The Schwarzschild coordinate rotation frequency at the marginally stable circular orbit, measured per unit time of a stationary clock at infinity. It scales inversely with black-hole mass. A finite-radius static clock adds a gravitational time-dilation factor; a quasi-periodic brightness signal need not directly equal this orbital frequency.
Articles by others on the same topic
The innermost stable circular orbit (ISCO) is a concept from general relativity that pertains to the orbits of objects around compact astrophysical objects, such as black holes or neutron stars. The ISCO represents the smallest orbit in which a test particle (like a small mass moving under gravitational influence) can stably orbit a massive body without spiraling into it due to gravitational or tidal forces. Here are key points about the ISCO: 1. **Stable vs.