  Kerr-AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiant
instabilities over a range of masses above extremality. We conjecture that
these instabilities settle down into Grey Galaxies (GGs) - a new class of
coarse-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 thermal
bulk gas that revolves around the centre of $AdS$ at the speed of light. The
gas carries a finite fraction of the total energy, as its parametrically low
energy density and large radius are inversely related. GGs exist at masses that
extend all the way down to the unitarity bound. Their thermodynamics is that of
a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their
boundary stress tensor is the sum of a smooth `black hole' contribution and a
peaked gas contribution that is delta function localized around the equator of
the boundary sphere in the large $N$ limit. We also construct another class of
solutions with the same charges; `Revolving Black Holes (RBHs)'. RBHs are
macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, and
consist of $\omega=1$ black holes revolving around the centre of $AdS$ at a
fixed radial location but in a quantum wave function in the angular directions.
RBH solutions are marginally entropically subdominant to GG solutions and do
not constitute the endpoint of the superradiant instability. Nonetheless, we
argue that supersymmetric versions of these solutions have interesting
implications for the spectrum of supersymmetric states in, e.g. ${\cal N}=4$
Yang-Mills theory.
