Abstract
There are strong interests in considering the ultra-light scalar field (especially axion) around a rapidly rotating black hole because of the possibility of observing a gravitational waves from axion condensate (axion cloud) around black hole. Motivated by this consideration, we study dynamics of ultra-light scalar field with self-interaction around a rapidly rotating black hole by the Renormalization group method. We found that for the relativistic cloud, saturation of the superradiant instability by the scattering of the axion due to the self-interaction does not occur in the weakly non-linear regime. This means that for the relativistic axion cloud, explosive phenomena called the Bosenova might happen in the realistic situation.
Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis neard= 4
