  Fluctuations of non-Abelian gauge fields in a background magnetic flux
contain tachyonic modes and hence the background is unstable. We extend these
results to the cases where the background flux is coupled to Einstein gravity
and show that the corresponding spherically symmetric geometries, which in the
absence of a cosmological constant are of the form of Reissner-Nordstrom
blackholes or the AdS_2xS^2, are also unstable. We discuss the relevance of
these instabilities to several places in string theory including various string
compactifications and the attractor mechanism. Our results for the latter imply
that the attractor mechanism shown to work for the extremal Abelian charged
blackholes, cannot be applied in a straightforward way to the extremal
non-Abelian colored blackholes.
