Neutron Star instabilities in full General Relativity using a $\Gamma=2.75$ ideal fluid

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 determine 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.