In this article, we studied the behavior of relativistic spherical objects considering Tolman IV spacetime in modified $f(R,\,T)$ gravity for the uncharged perfect fluid matter. We have chosen the matter Lagrangian as $\mathcal{ L}_m=-p$ to develop our present model. In particular, for this investigation we have reported for the compact object LMC $X-4$ [Mass=$(1.04 \pm 0.09)M_{ \odot}$; Radius= $8.301_{ -0.2}^{ +0.2}$ Km] in our paper. The effect of the coupling parameter $\beta$ on the local matter distribution of compact stars has been investigated in this paper. It can be seen that with greater values of $\beta$, the sound speed and adiabatic index are higher. On contrary, the mass function takes lower value for higher values of $\beta$. Our obtained solution does not admit singularities in the matter density, pressure and metric functions. According to our graphical analysis, this new stellar model satisfies all physical requirements anticipated in a realistic star.
Categories: gr-qc