Endpoints of Kerr-AdS superradiant instabilities and holography

Kerr-$AdS$ black holes develop superradiant instabilities if their angular velocity $\Omega > 1$, as their Hawking quanta get exponentially amplified in a ``Penrose-like'' process. These black holes must then decay into some other stable solutions. In this work we review the mechanism behind the superradiant instabilities and discuss some proposals for their endpoint, focusing in particular on Revolving Black Holes and Grey Galaxies. These solutions are built by ``storing'' part of the energy and angular momentum outside of the black hole itself, respectively into its center of mass motion and into a cloud of far away, large angular momentum field excitations. They extend the gravitational phase space from the extremality bound for black holes down to the unitarity bound of the dual CFT. We will show how several holographic arguments provide useful information on such solutions and help us to construct them.