  In this work we have discussed the implications of shear-free condition on
axially symmetric anisotropic gravitating objects in $f(R,T)$ theory.
Restricted axial symmetry ignoring rotation and reflection enteries is taken
into account for establishment of instability range. Implementation of linear
perturbation on constitutive modified dynamical equations yield evolution
equation. This equation associates adiabatic index $\Gamma$ with material and
dark source components defining stable and unstable regions in Newtonian (N)
and post-Newtonian (pN) approximations.
