Embedded Class-I Solution of Compact Stars in $f(R)$ Gravity with Karmarkar Condition

TL;DR

This study explores new embedded class-I solutions for compact stars within $f(R)$ gravity using the Karmarkar condition, analyzing physical viability and stability with observational data.

Contribution

It introduces a novel classification of solutions in $f(R)$ gravity for compact stars, employing the Karmarkar condition to relate metric potentials and validate models with observational data.

Findings

Models satisfy physical and stability conditions.

$f(R)$ gravity effectively describes compact star solutions.

Observational data supports model viability.

Abstract

This paper's main aim is to investigate the existence of a new classification of embedded class-I solutions of compact stars, by using Karmarkar condition in $f(R)$ gravity background. To achieve that goal, we consider two different models of the $f(R)$ theory of gravity for the static spherically symmetric spacetime by considering anisotropic matter distribution. Further, we employ Karmarkar condition to relate the two components of metric potentials $g_{rr}$ and $g_{tt}$. We assume a particular model for one metric potential and obtain the second one by Karmarkar condition. Moreover, we also calculate the values of constant parameters by using the observational data of these compact stars, namely, $Vela~ X-1,$ $PSR~J1614-2230,$ $4U~1608-52,$ $Cen~X-3$ and $4U~1820-30.$ We perform different physical tests like variational behavior of energy density and pressure components, stability and equilibrium conditions, energy constraints, mass function and adiabatic index to check the viability of $f(R)$ gravity models. All these physical attributes indicate the consistent behavior of our models. Our investigation also suggests that $f(R)$ theory of gravity appears as a suitable theory in describing the viability of a new classification of embedded class-I solutions of compact objects.