  5-dimensional Einstein-Maxwell-Chern-Simons theory with Chern-Simons
coefficient $\lambda=1$ has supersymmetric black holes with vanishing horizon
angular velocity, but finite angular momentum. Here supersymmetry is associated
with a borderline between stability and instability, since for $\lambda>1$ a
rotational instability arises, where counterrotating black holes appear, whose
horizon rotates in the opposite sense to the angular momentum. For $\lambda>2$
black holes are no longer uniquely characterized by their global charges, and
rotating black holes with vanishing angular momentum appear.
