Study of Embedded Class-I Fluid Spheres in $f(R,T)$ Gravity with Karmarkar Condition

TL;DR

This paper investigates the properties of embedded class-I fluid spheres within $f(R,T)$ gravity using the Karmarkar condition, applying a specific exponential model and analyzing stability and physical viability for certain compact stars.

Contribution

It introduces a novel approach combining $f(R,T)$ gravity with the Karmarkar condition to model anisotropic stellar objects and derives new solutions for specific compact stars.

Findings

Model is physically viable and stable for studied stars.

Derived metric potentials satisfy energy and stability conditions.

Results match observed properties of compact stars.

Abstract

In this article, we explore some emerging properties of the stellar objects in the frame of the $f(R,T)$ gravity by employing the well-known Karmarkar condition, where $R$ and $T$ represent Ricci scalar and trace of energy momentum tensor respectively. It is worthy to highlight here that we assume the exponential type model of $f(R,T)$ theory of gravity $f(R,T)=R+\alpha(e^{-\beta R}-1)+\gamma T$ along with the matter Lagrangian $\mathcal{L}_{m}=-\frac{1}{3}(p_{r}+2 p_{t})$ to classify the complete set of modified field equations. We demonstrate the embedded class-I technique by using the static spherically symmetric line element along with anisotropic fluid matter distribution. Further, to achieve our goal, we consider a specific expression of metric potential $g_{rr}$, already presented in literature, and proceed by using the Karmarkar condition to obtain the second metric potential. In particular, we use four different compact stars, namely $LMC~X-4,$ $EXO~1785-248,$ $Cen~X-3$ and $4U~1820-30$ and compute the corresponding values of the unknown parameters appearing in metric potentials. Moreover, we conduct various physical evolutions such as graphical nature of energy density and pressure progression, energy constraints, mass function, adiabatic index, stability and equilibrium conditions to ensure the viability and consistency of our proposed model. Our analysis indicates that the obtained anisotropic outcomes are physically acceptable with the finest degree of accuracy.