Anisotropic Tolman V Solutions by Decoupling Approach in $f(R,T^{2})$ Gravity

TL;DR

This paper develops anisotropic solutions in $f(R,T^{2})$ gravity using a minimal geometric deformation approach, analyzing their physical viability and stability for modeling compact stars like PSR J1614-2230.

Contribution

It introduces a novel decoupling method to generate anisotropic solutions in $f(R,T^{2})$ gravity based on Tolman V, expanding the toolkit for modeling compact objects.

Findings

First two solutions are viable for small decoupling parameters.

Third solution remains stable across all decoupling values.

Solutions satisfy energy conditions and match observed star properties.

Abstract

This paper investigates the behavior of anisotropic static spheres that are constructed by employing a minimal geometric deformation in the framework of $f(R,T^{2})$ gravity ($T^{2}=T_{\zeta\nu}T^{\zeta\nu}$, $R$ is the Ricci scalar and $T_{\zeta\nu}$ is the energy-momentum tensor). We consider a spherical setup with two sources: seed and additional. It is assumed that the seed source is isotropic whereas the new source is responsible for inducing anisotropy. We deform the $g_{rr}$ component to split the field equations into two sets. The first array corresponds to the isotropic solution whereas the second set contains the effect of the anisotropic source. The system related to isotropic source is determined by the metric potentials of Tolman V solution while three solutions of the second set are constructed corresponding to three different constraints. The physical acceptability of all solutions is checked through energy conditions by employing the radius and mass of PSR J1614-2230 star. We also examine the stability, mass, compactness and redshift of the obtained solutions. We conclude that first two solutions satisfy the viability and stability criteria only for small values of the decoupling parameter while third solution is stable for its all possible values.