Exploring physical properties of compact stars in \begin{document}${ f(R,T)}$\end{document} -gravity: An embedding approach

Solving field equations exactly in \begin{document}$f(R,T)-$\end{document} gravity is a challenging task. To do so, many authors have adopted different methods such as assuming both the metric functions and an equation of state (EoS) and a metric function. However, such methods may not always lead to well-behaved solutions, and the solutions may even be rejected after complete calculations. Nevertheless, very recent studies on embedding class-one methods suggest that the chances of arriving at a well-behaved solution are very high, which is inspiring. In the class-one approach, one of the metric potentials is estimated and the other can be obtained using the Karmarkar condition. In this study, a new class-one solution is proposed that is well-behaved from all physical points of view. The nature of the solution is analyzed by tuning the \begin{document}$f(R,T)-$\end{document} coupling parameter \begin{document}$\chi$\end{document} , and it is found that the solution leads to a stiffer EoS for \begin{document}$\chi=-1$\end{document} than that for \begin{document}$\chi=1$\end{document} . This is because for small values of \begin{document}$\chi$\end{document} , the velocity of sound is higher, leading to higher values of \begin{document}$M_{\rm max}$\end{document} in the \begin{document}$M-R$\end{document} curve and the EoS parameter \begin{document}$\omega$\end{document} . The solution satisfies the causality condition and energy conditions and remains stable and static under radial perturbations (static stability criterion) and in equilibrium (modified TOV equation). The resulting \begin{document}$M-R$\end{document} diagram is well-fitted with observed values from a few compact stars such as PSR J1614-2230, Vela X-1, Cen X-3, and SAX J1808.4-3658. Therefore, for different values of \begin{document}$\chi$\end{document} , the corresponding radii and their respective moments of inertia have been predicted from the \begin{document}$M-I$\end{document} curve.