In this work, we develop an algorithm to construct all static spherically symmetric anisotropic solutions for general relativistic polytropes. To this end, we follow the strategy presented by K. Lake in Phys. Rev. D 67 (2003) 104015 to obtain all static spherically symmetric perfect fluid solutions and then extended by L. Herrera el al., Phys. Rev. D 77 (2008) 027502 to the interesting case of locally anisotropic fluids. The formalism here developed requires the knowledge of only one function to generate all possible solutions. To illustrate the method, we obtain formal expressions for the generating functions of known polytopic solutions. Additionally, we obtain the generating function for both the conformally flat and class 1 polytropes.

中文翻译：

---

广义相对论多方体的所有静态球对称各向异性解

在这项工作中，我们开发了一种算法来构造广义相对论多方体的所有静态球对称各向异性解。为此，我们遵循 K. Lake 在 Phys 中提出的策略。Rev. D 67 (2003) 104015 以获得所有静态球对称完美流体解，然后由 L. Herrera 等人扩展，Phys。Rev. D 77 (2008) 027502 关于局部各向异性流体的有趣案例。这里开发的形式主义只需要了解一种功能即可生成所有可能的解决方案。为了说明该方法，我们获得了已知多面体解的生成函数的形式表达式。此外，我们获得了共形平面和 1 类多方体的生成函数。