  We present new results on dynamical instabilities in rapidly rotating
neutron-stars. In particular, using numerical simulations in full General
Relativity, we analyse the effects that the stellar compactness has on the
threshold for the onset of the dynamical bar-mode instability, as well as on
the appearance of other dynamical instabilities. By using an extrapolation
technique developed and tested in our previous study [1], we explicitly
determine the threshold for a wide range of compactnesses using four sequences
of models of constant baryonic mass comprising a total of 59 stellar models.
Our calculation of the threshold is in good agreement with the Newtonian
prediction and improves the previous post-Newtonian estimates. In addition, we
find that for stars with sufficiently large mass and compactness, the m=3
deformation is the fastest growing one. For all of the models considered, the
non-axisymmetric instability is suppressed on a dynamical timescale with an m=1
deformation dominating the final stages of the instability. These results,
together with those presented in [1], suggest that an m=1 deformation
represents a general and late-time feature of non-axisymmetric dynamical
instabilities both in full General Relativity and in Newtonian gravity.
