General isotropic charged fluid spheres within the matter coupling gravity formalism

In this paper, we proposed a new mathematical model of charged isotropic compact relativistic object in the $f(R,T)$ gravity. In the $f(R,T)$ framework, the gravitational action involves the trace of the energy–momentum tensor $T$ and the Ricci scalar $R$. We choose a specific $f(R,T)$ framework such that $f(R,T)=R+2\chi T$, in which $\chi$ represents the coupling parameter, which is responsible for measuring the deviation from the standard Einstein’s general theory of relativity (GR). A short overview of the modified $f(R,T)$ gravity theory is presented and the field equations are formulated in this novel modified gravity. It is shown that for a specific limit of the coupling parameter, the standard $GR$ can be restored from the considered $f(R,T)$ model. We modeled, mathematically, a specific charged compact star $XTEJ1739-217$ (M=1.51$M_{⨀}$, R=10.9 km), within the $f(R,T)$ extended gravity theory framework by taking benefit from the well studied Heintzmann IIa ansatz [H. Heintzmann, Z. Physik 228, 489–493 (1969)]. To examine the reliability and physical plausibility of Our model, different physical characteristics such as the energy density and pressure, electric field, energy conditions, stability analysis via Herrara cracking technique and the adiabatic index, equilibrium conditions under different forces, mass–radius relationship, compactness and surface red-shift are studied carefully, which are essential for confirming the model’s physical feasibility. The mathematically established results are more accurately represented by graphical illustrations for the various chosen values of the coupling parameter $\chi$. In this study, we also compared our findings with the standard GR results and the observational facts, and we inferred that for nonzero values of the coupling parameter, $\chi$, our results in $f(R,T)$ framework are closely related to the observational facts in comparison with the standard $GR$. We conclude that our presented model is well consistent with all the requirements and viably modeled the compact star $XTEJ1739-217$.