# Stability of Anisotropic Stellar Filaments

## TL;DR

This paper investigates the stability of anisotropic self-gravitating cylindrical celestial objects within $f(R,T)$ gravity, analyzing how perturbations and matter properties influence their collapse and instability regions.

## Contribution

It develops a framework for collapse equations in $f(R,T)$ gravity considering anisotropic matter and radial perturbations, highlighting the role of dark source terms and fluid rigidity.

## Key findings

- Unstable regions strongly depend on the fluid's stiffness parameter.
- Dark source terms in $f(R,T)$ gravity influence the instability of the system.
- Static profiles and matter variables control the collapse behavior.

## Abstract

The study of perturbation of self-gravitating celestial cylindrical object have been carried out in this paper. We have designed a framework to construct the collapse equation by formulating the modified field equations with the background of $f(R,T)$ theory as well as dynamical equations from the contracted form of Bianchi identities with anisotropic matter configuration. We have encapsulated the radial perturbations on metric and material variables of the geometry with some known static profile at Newtonian and post-Newtonian regimes. We examined a strong dependence of unstable regions on stiffness parameter which measures the rigidity of the fluid. Also, the static profile and matter variables with $f(R,T)$ dark source terms control the instability of compact cylindrical system.