Decoupled Anisotropic Buchdahl's Relativistic Models in $f(\mathbb{R},\mathbb{T})$ Theory

TL;DR

This paper develops three anisotropic relativistic star models within $f( ext{R}, ext{T})$ gravity using gravitational decoupling, extending isotropic solutions and analyzing their physical viability with observational data.

Contribution

It introduces a novel method to generate anisotropic solutions in $f( ext{R}, ext{T})$ gravity by decoupling the field equations and applying constraints, expanding the modeling toolkit.

Findings

Models II and III satisfy physical acceptability conditions.

The models are consistent with observational data for LMC X-4.

The approach effectively generates physically viable anisotropic stellar models.

Abstract

This paper constructs three different anisotropic extensions of the existing isotropic solution to the modified field equations through the gravitational decoupling in $f(\mathbb{R},\mathbb{T})$ theory. For this, we take a static sphere that is initially filled with the isotropic fluid and then add a new gravitational source producing anisotropy in the system. The field equations now correspond to the total matter configuration. We transform the radial metric component to split these equations into two sets characterizing their parent sources. The unknowns comprising in the first set are determined by considering the Buchdahl isotropic solution. On the other hand, we employ different constraints related to the additional gravitational source and make the second system solvable. Further, the constant triplet in Buchdahl solution is calculated by means of matching criteria between the interior and exterior geometries at the spherical boundary. The mass and radius of a compact star LMC X-4 are used to analyze the physical relevancy of the developed models. We conclude that our resulting models II and III are in well-agreement with acceptability conditions for the considered values of the parameters.