Study of Anisotropic Polytropes in $f(\mathcal{R},\mathrm{T})$ Theory

TL;DR

This study explores anisotropic polytropic stars within $f( ext{R}, ext{T})$ gravity, analyzing their structure, stability, and physical viability, and finds more stable models than in general relativity.

Contribution

It introduces a detailed formalism for anisotropic polytropes in $f( ext{R}, ext{T})$ gravity, including new solutions and stability analysis.

Findings

More viable and stable polytropic models are found compared to general relativity.

Anisotropic pressure significantly affects stellar structure and stability.

Physical behavior is validated through energy conditions and stability criteria.

Abstract

This paper examines the general formalism and applications of isotropic as well as anisotropic polytropic stars in curvature-matter coupled gravity. For this purpose, we consider static spherical and Schwarzschild spacetimes in the interior and exterior regions, respectively. We use two polytropic equations of state to obtain physically viable solutions of the field equations. The hydrostatic equilibrium and Lane-Emden equations are developed for both isotropic as well as anisotropic cases. We study the effects of anisotropic pressure on the stellar structure. Moreover, we graphically inspect the physical behavior of isotropic as well as anisotropic polytropes through energy conditions and stability criterion. Finally, we discuss Tolman mass to explore some characteristics of the models. It is concluded that more viable and stable polytropes are found in this theory as compared to general relativity.