The objective of this paper is to discuss anisotropic solutions representing static spherical self-gravitating systems in f(R) theory. We employ the extended gravitational decoupling approach and transform temporal as well as radial metric potentials which decomposes the system of non-linear field equations into two arrays: one set corresponding to seed source and the other one involves additional source terms. The domain of the isotropic solution is extended in the background of f(R) Starobinsky model by employing the metric potentials of Krori–Barua spacetime. We determine two anisotropic solutions by employing some physical constraints on the extra source. The values of unknown constants are computed by matching the interior and exterior spacetimes. We inspect the physical viability, equilibrium and stability of the obtained solutions corresponding to the star Her X-I. It is observed that one of the two extensions satisfies all the necessary physical requirements for particular values of the decoupling parameter.

本文的目的是讨论代表f ( R ) 理论中静态球形自引力系统的各向异性解。我们采用扩展的引力解耦方法并转换时间和径向度量势，将非线性场方程系统分解为两个数组：一组对应于种子源，另一组涉及额外的源项。各向同性解的域在f ( R) Starobinsky 模型通过使用 Krori-Barua 时空的度量势。我们通过对额外源采用一些物理约束来确定两个各向异性解决方案。未知常数的值是通过匹配内部和外部时空来计算的。我们检查了与 Her XI 星相对应的所得解的物理可行性、平衡性和稳定性。据观察，两个扩展之一满足去耦参数特定值的所有必要物理要求。