Black holes of mass M must have a spin angular momentum S below the Kerr limit ( \chi \equiv S / M ^ { 2 } \leq 1 ) , but whether astrophysical black holes can attain this limiting spin depends on their accretion history .
Gas accretion from a thin disk limits the black-hole spin to \chi _ { gas } \lesssim 0.9980 \pm 0.0002 , as electromagnetic radiation from this disk with retrograde angular momentum is preferentially absorbed by the black hole .
Extrapolation of numerical-relativity simulations of equal-mass binary black-hole mergers to maximum initial spins suggests these mergers yield a maximum spin \chi _ { eq } \lesssim 0.95 .
Here we show that for smaller mass ratios q \equiv m / M \ll 1 , the superradiant extraction of angular momentum from the larger black hole imposes a fundamental limit \chi _ { lim } \lesssim 0.9979 \pm 0.0001 on the final black-hole spin even in the test-particle limit ( q \to 0 ) of binary black-hole mergers .
The nearly equal values of \chi _ { gas } and \chi _ { lim } imply that measurement of supermassive black-hole spins can not distinguish a black hole built by gas accretion from one assembled by the gravitational inspiral of a disk of compact stellar remnants .
We also show how superradiant scattering alters the mass and spin predicted by models derived from extrapolating test-particle mergers to finite mass ratios .