  Black branes and strings are generally unstable against a certain sector of
gravitational perturbations. This is known as the Gregory-Laflamme instability.
It has been recently argued that there exists another general instability
affecting many rotating extended black objects. This instability is in a sense
universal, in that it is triggered by any massless field, and not just
gravitational perturbations. Here we investigate this novel mechanism in
detail. For this instability to work, two ingredients are necessary: (i) an
ergo-region, which gives rise to superradiant amplification of waves, and (ii)
``bound'' states in the effective potential governing the evolution of the
particular mode under study. We show that the black brane Kerr_4 x R^p is
unstable against this mechanism, and we present numerical results for
instability timescales for this case. On the other hand, and quite
surprisingly, black branes of the form Kerr_d x R^p are all stable against this
mechanism for d>4. This is quite an unexpected result, and it stems from the
fact that there are no stable circular orbits in higher dimensional black hole
spacetimes, or in a wave picture, that there are no bound states in the
effective potential. We also show that it is quite easy to simulate this
instability in the laboratory with acoustic black branes.
