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We study the superradiant instability of a massive boson around a spinningblack hole in full general relativity without assuming spatial symmetries. Wefocus on the case of a rapidly spinning black hole in the presence of a vectorboson with a Compton wavelength comparable to the black hole radius, which isthe regime where relativistic effects are maximized. We follow the growth ofthe boson cloud through superradiance into the nonlinear regime as it spinsdown the black hole, reaches a maximum energy, and begins to dissipate throughthe emission of gravitational waves. We find that the superradiant instabilitycan efficiently convert a significant fraction of a black hole's rotationalenergy into gravitational radiation.

Massive Boson Superradiant Instability of Black Holes: Nonlinear Growth, Saturation, and Gravitational Radiation