Nonlinear Instability in Gravitational Euler-Poisson system for $\gamma =6\mathrm{/}5$

The dynamics of gaseous stars can be described by the Euler-Poisson system. Inspired by Rein’s stability result for $\gamma >4\mathrm{/}3$, we prove the nonlinear instability of steady states for the adiabatic exponent $\gamma =6\mathrm{/}5$ in spherically symmetric and isentropic motion.