Dynamical Analysis of Self-gravitating Stars in Modified Gauss-Bonnet Gravity

In this paper, we have continued the work of Herrera \emph{et al.} \cite{herrera2012dynamical} in $f(G)$ gravitational theory. For this purpose, a spherically symmetric fluid exhibiting locally anisotropic pressure along with the energy density, is taken under consideration. The perturbation scheme is imposed on modified field equations and the dynamical equations. The collapse equation is devised from these perturbed equations which stimulates to disclose the instability zone under both Newtonian and post-Newtonian constraints. It is wrapped up by concluding that dynamical instability is interpreted by the adiabatic index $\Gamma$ which relies on the anisotropic pressure, energy density and the dark source terms due to $f(G)$ gravity.