  In collisions of heavy ions at extremely high energies, it is possible for a
significant quantity of angular momentum to be deposited into the Quark-Gluon
Plasma which is thought to be produced. We develop a simple geometric model of
such a system, and show that it is dual, in the AdS/CFT sense, to a rotating
AdS black hole with a topologically planar event horizon. However, when this
black hole is embedded in string theory, it proves to be unstable, for all
non-zero angular momenta, to a certain non-perturbative effect: the familiar
planar black hole, as used in most AdS/CFT analyses of QGP physics, is
"fragile". The upshot is that the AdS/CFT duality apparently predicts that the
QGP should always become unstable when it is produced in peripheral collisions.
However, we argue that holography indicates that relatively low angular momenta
delay the development of the instability, so that in practice it may be
observable only for peripheral collisions involving favourable impact
parameters, generating extremely large angular momenta. The result may be
holographic prediction of a cutoff for the observable angular momenta of the
QGP, or perhaps of an analogous phenomenon in condensed matter physics.
