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

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