Stability of a Class of Non-Static Axial Self-Gravitating Systems in $f(R)$ Gravity

TL;DR

This paper investigates the stability of non-static, axially symmetric self-gravitating systems in $f(R)$ gravity, analyzing how physical parameters influence instability regions in different gravitational regimes.

Contribution

It introduces a stability analysis of axially symmetric systems in $f(R)$ gravity considering anisotropic matter and perturbations from hydrostatic equilibrium.

Findings

Stability regions depend on pressure anisotropy, energy density, and higher curvature terms.

Instability ranges are influenced by the stiffness parameter $\Gamma_1$.

Physical parameter profiles affect the onset of dynamical instability.

Abstract

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider $f(R)=R+{\epsilon}R^2$ model and assume hydrostatic equilibrium of the axial self-gravitating system at large past time. Considering perturbation from hydrostatic phase, we develop dynamical as well as collapse equations and explore dynamical instabilities at Newtonian and post-Newtonian regimes. It is concluded with the help of stiffness parameter, $\Gamma_1$, that radial profile of physical parameters like pressure anisotropy, energy density and higher curvature terms of the $f(R)$ model affect the instability ranges.