Impact of extended Starobinsky model on evolution of anisotropic, vorticity-free axially symmetric sources

We study the implications of R-n extension of Starobinsky model on dynamical instability of Vorticity-free axially symmetric gravitating body. The matter distribution is considered to be anisotropic for which modified field equations are formed in context of f(R) gravity. In order to achieve the collapse equation, we make use of the dynamical equations, extracted from linearly perturbed contracted Bianchi identities. The collapse equation carries adiabatic index Gamma in terms of usual and dark source components, defining the range of stability/insatbility in Newtonian (N) and post-Newtonian (pN) eras. It is found that supersymmetric supergravity f(R) model represents the more practical substitute of higher order curvature corrections.