Employing the Palatini version of $f(R)$ gravity theory ($R$ being the Ricci scalar), this paper describes the evolution of a radiating axially symmetric fluid and its changeover to a non-radiating state. Orthonormal tetrad formalism is taken into account because this technique is easier to use and yields simple tensors leaving the predictions of the theory unchanged. Effective tetrad components of the heat flux, the vorticity vector and the shear tensor are evaluated along with the two parts (electric and magnetic) of Weyl curvature tensor. Furthermore, certain structure scalars are procured from the orthogonal division of the Riemann tensor to figure out basic characteristics of the fluid source like the energy density, stress anisotropy and the heat flux. Few differential equations are worked out to gain insight into the consistency of modified field equations while the system transits from its radiating to equilibrium state.

使用 Palatini 版本$F(R)$重力理论（$R$作为 Ricci 标量），本文描述了辐射轴对称流体的演化及其向非辐射状态的转变。正交四分体形式主义被考虑在内，因为这种技术更易于使用并且产生简单的张量而使理论的预测保持不变。热通量、涡量矢量和剪切张量的有效四分体分量与 Weyl 曲率张量的两个部分（电和磁）一起进行评估。此外，从黎曼张量的正交分割中获得某些结构标量，以计算出流体源的基本特征，如能量密度、应力各向异性和热通量。