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Kerr-AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiantinstabilities over a range of masses above extremality. We conjecture thatthese instabilities settle down into Grey Galaxies (GGs) - a new class ofcoarse-grained solutions to Einstein's equations which we construct in $d=3$.Grey Galaxies are made up of a black hole with critical angular velocity$\omega=1$ in the `centre' of $AdS$, surrounded by a large flat disk of thermalbulk gas that revolves around the centre of $AdS$ at the speed of light. Thegas carries a finite fraction of the total energy, as its parametrically lowenergy density and large radius are inversely related. GGs exist at masses thatextend all the way down to the unitarity bound. Their thermodynamics is that ofa weakly interacting mix of Kerr-AdS black holes and the bulk gas. Theirboundary stress tensor is the sum of a smooth `black hole' contribution and apeaked gas contribution that is delta function localized around the equator ofthe boundary sphere in the large $N$ limit. We also construct another class ofsolutions with the same charges; `Revolving Black Holes (RBHs)'. RBHs aremacroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, andconsist of $\omega=1$ black holes revolving around the centre of $AdS$ at afixed radial location but in a quantum wave function in the angular directions.RBH solutions are marginally entropically subdominant to GG solutions and donot constitute the endpoint of the superradiant instability. Nonetheless, weargue that supersymmetric versions of these solutions have interestingimplications for the spectrum of supersymmetric states in, e.g. ${\cal N}=4$Yang-Mills theory.

'Grey Galaxies' as an endpoint of the Kerr-AdS superradiant instability