Stability of anisotropic stellar filaments

The study of perturbation of self-gravitating celestial cylindrical object have been carried out in this paper. We have designed a framework to construct the collapse equation by formulating the modified field equations with the background of $f(R,T)$ theory as well as dynamical equations from the contracted form of Bianchi identities with anisotropic matter configuration. We have encapsulated the radial perturbations on metric and material variables of the geometry with some known static profile at Newtonian and post-Newtonian regimes. We examined a strong dependence of unstable regions on stiffness parameter which measures the rigidity of the fluid. Also, the static profile and matter variables with $f(R,T)$ dark source terms control the instability of compact cylindrical system.