Superradiant instabilities in black hole systems

A wave impinging on a Kerr black hole can be amplified as it scatters off the hole if certain conditions are satisfied. This is known as superradiant scattering. By building a mirror around the black hole one can make the system unstable. This is the black hole bomb of Press and Teukolsky. We investigate in detail this process and compute the growing timescales and oscillation frequencies as a function of the mirror's location. It is found that in order for the system, black hole plus mirror, to become unstable there is a minimum distance at which the mirror must be located. We also show with an explicit example that such a bomb can be built, once an appropriate black hole is located. Now, a spacetime with a "mirror" naturally incorporated in it is anti-de Sitter (AdS) spacetime, since the AdS space behaves effectively as a box with a reflecting gravitational wall at its infinity. Thus, a small Kerr-AdS black hole is naturally unstable to superradiant scattering of a wave that is generated in its vicinity.