Superradiant instabilities in astrophysical systems
  Light bosonic degrees of freedom have become a serious candidate for dark
matter. The evolution of these fields around curved spacetimes is poorly
understood but is expected to display interesting effects. In particular, the
interaction of light bosonic fields with supermassive black holes, key players
in most galaxies, could provide colourful examples of superradiance and
nonlinear bosenova-like collapse. In turn, the observation of spinning black
holes is expected to impose stringent bounds on the mass of putative massive
bosonic fields in our universe. Our purpose here is to present a comprehensive
study of the evolution of linearized massive scalar and vector fields in the
vicinities of rotating black holes. For a certain boson field mass range, the
field can become trapped in a potential barrier outside the horizon and
transition to a bound state. Because there are a number of such quasi-bound
states, the generic outcome is an amplitude modulated sinusoidal, or beating,
signal. We believe that the appearance of such beatings has gone unnoticed in
the past, and in fact mistaken for exponential growth. The amplitude modulation
of the signal depends strongly on the relative excitation of the overtones,
which in turn is strongly tied to the bound-state geography. For the first time
we explore massive vector fields in generic BH background which are hard, if
not impossible, to separate in the Kerr background. Our results show that
spinning BHs are generically strongly unstable against massive vector fields.
