  The evolution of small perturbations around rotating black branes and
strings, which are low energy solutions of string theory, are investigated. For
simplicity, we concentrate on the Kerr solution times transverse flat extra
dimensions, possibly compactified, but one can also treat other branes composed
of any rotating black hole and extra transverse dimensions, as well as analogue
black hole models and rotating bodies in fluid mechanics systems. It is shown
that such a rotating black brane is unstable against any massless (scalar,
vectorial, tensorial or other) field perturbation for a wide range of
wavelengths and frequencies in the transverse dimensions. Since it holds for
any massless field it can be considered, in this sense, a stronger instability
than the one studied by Gregory and Laflamme. Accordingly, it has also a
totally different physical origin. The perturbations can be stabilized if the
extra dimensions are compactified to a length smaller than the minimum
wavelength for which the instability settles in, resembling in this connection
the Gregory-Laflamme case. Likewise, this instability will have no effect for
astrophysical black holes. However, in the large extra dimensions scenario,
where TeV scale black holes can be produced, this instability should be
important. It seems plausible that the endpoint of this instability is a
static, or very slowly rotating, black brane and some outgoing radiation at
infinity.
