Anisotropic spheres via embedding approach in $\mathcal{R}+\beta\mathcal{R}^{2}$ gravity with matter coupling

TL;DR

This paper models anisotropic compact stars within a modified gravity framework using embedding class-1 solutions, demonstrating their physical viability and stability with observational data.

Contribution

It introduces a novel approach combining embedding class-1 solutions with $f( ext{R}, ext{T})$ gravity to analyze anisotropic star profiles.

Findings

Stars are physically realistic and stable.

Models are free from singularities.

Results agree with observational data.

Abstract

The manifesto of the current article is to investigate the compact anisotropic matter profiles in the context of one of the modified gravitational theories, known as $f(\mathcal{R}, \mathcal{T})$ gravity, where $\mathcal{R}$ is a Ricci Scalar and $\mathcal{T}$ is the trace of the energy-momentum tensor. To achieve the desired goal, we capitalized on the spherical symmetric space-time and utilized the embedding class-1 solution via Karmarkar's condition in modeling the matter profiles. To calculate the unidentified constraints, Schwarzschild exterior solution along with experimental statistics of three different stars LMC X-4, Cen X-3, and EXO 1785-248 are taken under consideration. For the evaluation of the dynamical equations, a unique model $f(\mathcal{R}, \mathcal{T})=\mathcal{R}+\beta \mathcal{R}^2+\lambda \mathcal{T}$ has been considered, with $\beta$ and $\lambda$ being the real constants. Different physical aspects have been exploited with the help of modified dynamical equations. Conclusively, all the stars under observations are realistic, stable, and are free from all singularities.