Abstract
In this work, we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in [Formula: see text] theory. Restricted axial symmetry ignoring rotation and reflection entries containing three independent metric functions 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 [Formula: see text] with material and dark source components of physical parameters defining stable and unstable regions in Newtonian (N) and post-Newtonian (pN) approximations. It is remarked that the axial system evolving under shear-free condition implicates high levels of stability in anisotropic environment.
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