Stability analysis of axial reflection symmetric spacetime

Abstract

In this paper, we explore instability regions of non-static axial reflection symmetric spacetime with anisotropic source in the interior. We impose linear perturbation on the Einstein field equations and dynamical equations to establish the collapse equation. The effects of different physical factors like energy density and anisotropic stresses on the instability regions are studied under Newtonian and post-Newtonian limits. We conclude that stiffness parameter has a significant role in this analysis while the reflection terms increase instability ranges of non-static axial collapse.