In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the [Formula: see text] gravity with the aid of some algebraic techniques. The extracted solutions are then utilized in order to get conformal vector fields (CVFs). It is important to mention that the adopted techniques enable us to obtain various classes of space-times with viable [Formula: see text] gravity models which already exist in the literature. Excluding all such classes, we find that there exist three cases for which the space-times admit proper CVFs, whereas in rest of the cases, CVFs become KVFs. We have also highlighted some physical implications of our obtained results.

中文翻译：

---

修正远平行引力理论中静态球对称完美流体时空的共形矢量场

在本文中，我们首先借助一些代数技术求解[公式：见正文]重力中静态球面（SS）对称完美流体时空的爱因斯坦场方程（EFE）。然后利用提取的解决方案来获得保形矢量场 (CVF)。值得一提的是，所采用的技术使我们能够通过文献中已经存在的可行[公式：见文本]重力模型获得各种类别的时空。排除所有这些类，我们发现存在时空允许正确 CVF 的三种情况，而在其余情况下，CVF 变为 KVF。我们还强调了我们获得的结果的一些物理意义。