Stability analysis of cylindrically symmetric self-gravitating systems in R plus εR2 gravity

This paper performs stability analysis of an adiabatic anisotropic cylindrical collapsing system in metric f(R) gravity. We construct general collapse equation from the dynamical equation through perturbation scheme. It is found that the dynamical stability of the system evolving with and without expansion at both Newtonian as well as post-Newtonian orders is controlled by the extra curvature f(R) gravity terms, radial density profile and pressure of the fluid. We conclude that the adiabatic index Gamma(1) or stiffness parameter plays a key role only if the system evolves with expansion scalar. We also reduce our solutions to constant curvature as well as f(R) -> R limits.