Superluminal neutrinos and the tachyon's stability in the rotating Universe

It is well-known that a hypothetical particle which moves faster than the light, a \emph{tachyon}, is unstable in the Minkowski space-time. Here we shall show that, contrary to the Minkowski case, the tachyon is stable in the rotating Universe described by a family of the G"{o}del-like solutions, unless the absolute value of its mass is larger than some small constant which is related to the universes rotation scale and is many orders less than the electrons mass. The smallness of this upper bound on the tachyon`s mass might be an explanation why we do not observe heavy tachyons. Mathematically, the stability bound is similar to the well-known Breitenlohner-Freedman bound for the asymptotically anti-de Sitter (AdS) space-times.