# Role of $f(R,T,R_{\mu\nu}T^{\mu\nu})$ Model on the Stability of Cylindrical Stellar Model

## TL;DR

This paper examines the stability and instability conditions of cylindrical stellar models within a modified gravity framework, highlighting the influence of dark source terms and the adiabatic index on stellar stability.

## Contribution

It introduces a perturbation analysis of non-static anisotropic cylindrical stars in $f(R,T,R_{ ext{μν}}T^{ ext{μν}})$ gravity, emphasizing the role of dark sources and adiabatic index in stability.

## Key findings

- Dark source terms significantly affect stability conditions.
- Adiabatic index determines stability regimes in modified gravity.
- Instability constraints are derived for Newtonian and post-Newtonian limits.

## Abstract

The aim of this paper is to investigate the stable/unstable regimes of the non-static anisotropic filamentary stellar models in the framework of $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity. We construct the field equations and conservation laws in the perspective of this gravity. The perturbation scheme is applied to analyze the behavior of a particular $f(R,T,R_{\mu\nu}T^{\mu\nu})$ cosmological model on the evolution of cylindrical system. The role of adiabatic index is also checked in the formulations of instability regions. We have explored the instability constraints at Newtonian and post-Newtonian limits. Our results reinforce the significance of adiabatic index and dark source terms in the stability analysis of celestial objects in modified gravity.