We present results on the effect of the stiffness of the equation of state on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change in the threshold for the emerg
ence of the instability for a range of the adiabatic $Gamma$ index from 2.0 to 3.0, including two values chosen to mimic more realistic equations of state at high densities.
We present results about the effect of the use of a stiffer equation of state, namely the ideal-fluid $Gamma=2.75$ ones, on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We deter
mine the change on the critical value of the instability parameter $beta$ for the emergence of the instability when the adiabatic index $Gamma$ is changed from 2 to 2.75 in order to mimic the behavior of a realistic equation of state. In particular, we show that the threshold for the onset of the bar-mode instability is reduced by this change in the stiffness and give a precise quantification of the change in value of the critical parameter $beta_c$. We also extend the analysis to lower values of $beta$ and show that low-beta shear instabilities are present also in the case of matter described by a simple polytropic equation of state.
