  We investigate the Gregory-Laflamme instability for black strings carrying
KK-momentum along the internal direction. We demonstrate a simple kinematical
relation between the thresholds of the classical instability for the boosted
and static black strings. We also find that Sorkin's critical dimension depends
on the internal velocity and in fact disappears for sufficiently large boosts.
Our analysis implies the existence of an analogous instability for the
five-dimensional black ring of Emparan and Reall. We also use our results for
boosted black strings to construct a simple model of the black ring and argue
that such rings exist in any number of space-time dimensions.
