This manuscript is devoted to a general study on axial and reflection-symmetric self-gravitating sources in the background of $f(R,T)$ gravity, where $T$ represents the trace of stress energy-tensor, while $R$ is the Ricci scalar. For this purpose, all the fundamental equations and notions set to carry out the general study are established. The corresponding field, as well as dynamical equations, are also exhibited. In order to discuss the thermodynamics aspects of the selected system, the modified transport equation is presented. The Weyl-tensor is utilized to evaluate the generalized version of scalar variables termed structure scalars. To produce modified scalar equations, we employ the structure scalars. The applications of our obtained results are examined on the dynamics of the source in $f(R,T)$ gravity. We conclude that the modified structure scalars play an important role in the dynamics of compact objects.

这份手稿致力于对轴和反射对称自引力源的一般研究 $F(\mathrm{电阻},吨)$ 重力，其中 $吨$ 表示应力能量张量的迹，而 $\mathrm{电阻}$是 Ricci 标量。为此，建立了用于进行一般研究的所有基本方程和概念。还展示了相应的场以及动力学方程。为了讨论所选系统的热力学方面，提出了修正的输运方程。Weyl-tensor 用于评估称为结构标量的标量变量的广义版本。为了产生修正的标量方程，我们使用结构标量。我们获得的结果的应用在源的动力学上进行了检查$F(\mathrm{电阻},吨)$重力。我们得出结论，修改后的结构标量在紧凑物体的动力学中起着重要作用。