  Black hole solutions that are asymptotic to $ AdS_5 \times S^5$ or $ AdS_4
\times S^7$ can rotate in two different ways. If the internal sphere rotates
then one can obtain a Reissner-Nordstrom-AdS black hole. If the asymptotically
AdS space rotates then one can obtain a Kerr-AdS hole. One might expect
superradiant scattering to be possible in either of these cases. Superradiant
modes reflected off the potential barrier outside the hole would be
re-amplified at the horizon, and a classical instability would result. We point
out that the existence of a Killing vector field timelike everywhere outside
the horizon prevents this from occurring for black holes with negative action.
Such black holes are also thermodynamically stable in the grand canonical
ensemble. The CFT duals of these black holes correspond to a theory in an
Einstein universe with a chemical potential and a theory in a rotating Einstein
universe. We study these CFTs in the zero coupling limit. In the first case,
Bose-Einstein condensation occurs on the boundary at a critical value of the
chemical potential. However the supergravity calculation demonstrates that this
is not to be expected at strong coupling. In the second case, we investigate
the limit in which the angular velocity of the Einstein universe approaches the
speed of light at finite temperature. This is a new limit in which to compare
the CFT at strong and weak coupling. We find that the free CFT partition
function and supergravity action have the same type of divergence but the usual
factor of 4/3 is modified at finite temperature.
