This manuscript aims to discuss the factors holding in/stability of axially symmetric compact system with anisotropic environment in the background of $f(R,T)$ gravity, where $R$ is invariant Ricci curvature and $T$ stands for trace of energy–momentum tensor. We constituted field and conservation equations in the background of $f(R,T)$ gravity. To establish the collapse equation, we make use of perturbation for all the variables involving in conservation equations, field equations, extra curvature terms of modified gravity and the particular $f(R,T)$ model. To estimate dynamical in/stability of celestial compact system, we acquired some meaningful constraints for adiabatic index $\gamma$ in Newtonian and Post Newtonian domains. Also, some constraints are imposed on physical quantities to maintain the stability of celestial self-gravitating astrophysical configuration.

该手稿旨在探讨在各向异性环境下轴对称致密系统的保持稳定性的因素。 $F（\mathrm{[R}，Ť）$ 重力在哪里 $\mathrm{[R}$ 是不变的Ricci曲率和 $Ť$代表能量-动量张量的痕迹。我们在背景下构造了场和守恒方程$F（\mathrm{[R}，Ť）$重力。为了建立坍塌方程，我们对守恒方程，场方程，修正重力的额外曲率项以及特定$F（\mathrm{[R}，Ť）$模型。为了估算天体致密系统的动力不稳定性，我们获得了绝热指数的一些有意义的约束$\gamma$在牛顿域和后牛顿域中。而且，对物理量施加了一些限制，以保持天体自重天体构造的稳定性。