  It has long been known that, in higher-dimensional general relativity, there
are black hole solutions with an arbitrarily large angular momentum for a fixed
mass. We examine the geometry of the event horizon of such ultra-spinning black
holes and argue that these solutions become unstable at large enough rotation.
Hence we find that higher-dimensional general relativity imposes an effective
`Kerr-bound' on spinning black holes through a dynamical decay mechanism. Our
results also give indications of the existence of new stationary black holes
with `rippled' horizons of spherical topology. We consider various scenarios
for the possible decay of ultra-spinning black holes, and finally discuss the
implications of our results for black holes in braneworld scenarios.
