# Role of $\sigma R^{2}+\gamma R_{\mu\nu}T^{\mu\nu}$ Model on Anisotropic Polytropes

## TL;DR

This study explores how a specific modified gravity model influences the structure and stability of anisotropic polytropic stars, revealing that such stars remain stable and within observational mass limits.

## Contribution

It introduces a numerical analysis of anisotropic stellar models within $f(R,T,Q)$ gravity, focusing on the effects of the $\sigma R^{2}+\gamma Q$ model on stellar properties.

## Key findings

- Polytropic stars are stable under the model.
- Maximum stellar mass remains within Chandrasekhar limit.
- Physical conditions like energy and causality are satisfied.

## Abstract

This paper analyzes the anisotropic stellar evolution governed by a polytropic equation of state in the framework of $f(R,T,Q)$ gravity, where $Q=R_{ab}T^{ab}$. We construct the field equations, hydrostatic equilibrium equation and trace equation to obtain their solutions numerically under the influence of $\sigma R^{2}+\gamma Q$ gravity model, where $\sigma$ and $\gamma$ are arbitrary constants. We examine the dependence of various physical characteristics such as radial/tangential pressure, energy density, anisotropic factor, total mass and surface redshift for specific values of the model parameters. The physical acceptability of the considered model is discussed by verifying the validity of energy conditions, causality condition, and adiabatic index. We also study the effects arising due to the strong non-minimal matter-curvature coupling on anisotropic polytropes. It is found that the polytropic stars are stable and their maximum mass point lies within the required observational Chandrasekhar limit.