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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., Comment: 12 pages, 10 figures, Accepted for publication in Chinese Journal of Physics

This work aims to investigate the behaviour of compact stars in the background of $f(R, T)$ theory of gravity. For current work, we consider the Krori-Barua metric potential i.e., $\nu(r)= Br^2+C$ and $\lambda(r)= Ar^2,$ where, $A, B$ and $C$ are constants. We use matching conditions of spherically symmetric space-time with Schwarzschild solution as an exterior geometry and examine the physical behaviour of stellar structure by assuming the exponential type $f(R, T)$ gravity model. In the present analysis, we discuss the graphical behaviour of energy density, radial pressure, tangential pressure, equation of state parameters, anisotropy and stability analysis respectively. Furthermore, an equilibrium condition can be visualized through the modified Tolman-Oppenheimer-Volkov equation. Some extra features of compact stars i.e. mass-radius function, compactness factor and surface redshift have also been investigated. Conclusively, all the results in current study validate the existence of compact stars under exponential $f(R, T)$ gravity model., Comment: 11 pages, 9 figures