# Dynamical Analysis of Cylindrically Symmetric Anisotropic Sources in $f(R,T)$ Gravity

## TL;DR

This paper investigates the stability of cylindrically symmetric, anisotropic collapsing objects within $f(R,T)$ gravity, deriving conditions for stability and analyzing how physical parameters influence collapse in different regimes.

## Contribution

It introduces a stability analysis framework for anisotropic cylinders in $f(R,T)$ gravity, including derived dynamical equations and instability conditions in Newtonian and post-Newtonian regimes.

## Key findings

- Instability range depends on physical parameters and adiabatic index.
- Conditions for stability are established based on physical quantities.
- Collapse behavior varies between Newtonian and post-Newtonian regimes.

## Abstract

In this paper, we have analyzed the stability of cylindrically symmetric collapsing object filled with locally anisotropic fluid in $f(R,T)$ theory, where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor of matter. Modified field equations and dynamical equations are constructed in $f(R,T)$ gravity. Evolution or collapse equation is derived from dynamical equations by performing linear perturbation on them. Instability range is explored in both Newtonian and post-Newtonian regimes with the help of adiabetic index, which defines the impact of physical parameters on the instability range. Some conditions are imposed on physical quantities to secure the stability of the gravitating sources.