Innermost stable circular orbit

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The last orbit matter can hold before it must fall. Newtonian gravity permits a stable circular orbit at any radius; general relativity does not, and below a critical radius every circular orbit is unstable, so an inspiralling particle spirals in over a few orbits rather than drifting slowly. For a non-rotating black hole the radius is six GM over c-squared - three Schwarzschild radii - and it moves inward for prograde orbits around a spinning hole, approaching the horizon in the extremal limit. This single number sets the efficiency of accretion, because it fixes how much gravitational binding energy can be radiated before the material is lost. About 5.7 per cent of the rest mass for a non-rotating hole, and up to something over 40 per cent for a maximally spinning one. Hydrogen fusion converts about 0.7 per cent. That comparison is why accretion onto black holes is the most efficient sustained energy release known in astrophysics. Not a place on Earth.

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