Instability of Meridional Axial System in f(R) Gravity

TL;DR

This paper investigates the dynamical instability of non-static axial stellar structures in $f(R)$ gravity, revealing how modified gravity terms influence stability conditions at different approximations.

Contribution

It introduces a generalized Euler's equation in $f(R)$ gravity and analyzes the instability constraints for axial stellar systems.

Findings

$f(R)$ terms can induce stability in stellar structures.

Instability depends on static profile coefficients.

Stability is influenced by $f(R)$ curvature modifications.

Abstract

We analyze dynamical instability of non-static reflection axial stellar structure by taking into account generalized Euler's equation in metric $f(R)$ gravity. Such an equation is obtained by contracting Bianchi identities of usual anisotropic and effective stress-energy tensors, which after using radial perturbation technique gives modified collapse equation. In the realm of $R+\epsilon R^n$ gravity model, we investigate instability constraints at Newtonian and post-Newtonian approximations. We find that instability of meridional axial self-gravitating system depends upon static profile of structure coefficients while $f(R)$ extra curvature terms induce stability to the evolving celestial body.