Extended Decoupled Anisotropic Solutions in $f(\mathcal{R},\mathcal{T},\mathcal{R}_{\gamma\chi}\mathcal{T}^{\gamma\chi})$ Gravity

TL;DR

This paper develops anisotropic solutions in extended $f(R,T,R_{γχ}T^{γχ})$ gravity using gravitational decoupling, analyzing their physical viability and stability through graphical methods.

Contribution

It introduces a novel application of extended gravitational decoupling to generate anisotropic solutions in a complex modified gravity framework.

Findings

Solutions satisfy energy conditions.

Stable behavior observed for pressure-like constraint.

Physical variables are significantly affected by the decoupling parameter.

Abstract

In this paper, we consider static spherical structure to develop some anisotropic solutions by employing the extended gravitational decoupling scheme in the background of $f(\mathcal{R},\mathcal{T},\mathcal{R}_{\gamma\chi}\mathcal{T}^{\gamma\chi})$ gravity, where $\mathcal{R}$ and $\mathcal{T}$ indicate the Ricci scalar and trace of the energy-momentum tensor, respectively. We transform both radial as well as temporal metric functions and apply them on the field equations that produce two different sets corresponding to the decoupling parameter $\xi$. The first set is associated with isotropic distribution, i.e., modified Krori-Barua solution. The second set is influenced from anisotropic factor and contains unknowns which are determined by taking some constraints. The impact of decoupling parameter is then analyzed on the obtained physical variables and anisotropy. We also investigate energy conditions and some other parameters such as mass, compactness and redshift graphically. It is found that our solution corresponding to pressure-like constraint shows stable behavior throughout in this gravity for the considered range of $\xi$.