This paper uses pure geometric field theory to construct a stellar model for a static spherically symmetric anisotropic compact star. The expression pure geometry means that all physical quantities and fields are defined in terms of the geometric objects of the geometry used. This implies the possibility of defining the material-energy tensor geometrically, not phenomenologically, from the geometry under consideration, absolute parallelism (AP-) geometry. Two solutions are obtained for the field equations of the theory, an interior solution and an exterior solution. The stellar model is obtained as an analytical solution of the field equations within the material distribution. An equation of state for anisotropic material distribution is derived from the model rather than being imposed on it. The vacuum solution of the field equations coincides with the Schwarzschild exterior solution. Matching the interior and exterior solutions at the boundary of the stellar configuration enables fixing the integration constants. The physical acceptability and stability analysis of the model are discussed, and the results show that the present model is suitable for studying the envelope region of a neutron star in a core-envelope type model. The model is investigated graphically using the estimated data of the pulsar 4U1820-30 with mass and radius 9.1 km. In conclusion, this study demonstrates the feasibility of constructing a pure geometric stellar model and highlights the benefits of using such an approach to understand stellar structure.

中文翻译：

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致密星的结构：纯几何方法

本文利用纯几何场论构建了静态球对称各向异性致密星的恒星模型。纯几何这一表述意味着所有物理量和物理场都是根据所使用的几何的几何对象来定义的。这意味着可以根据所考虑的几何学，即绝对平行（AP-）几何学，以几何学而非唯象学的方式定义物质能量张量。获得了理论场方程的两个解：内部解和外部解。恒星模型是作为材料分布内场方程的解析解而获得的。各向异性材料分布的状态方程是从模型中导出的，而不是强加于模型的。场方程的真空解与史瓦西外解一致。在恒星结构的边界处匹配内部和外部解可以固定积分常数。讨论了模型的物理可接受性和稳定性分析，结果表明该模型适用于研究核-包络型模型中中子星的包络区。使用质量和半径为 9.1 km 的脉冲星 4U1820-30 的估计数据对该模型进行了图形研究。总之，这项研究证明了构建纯几何恒星模型的可行性，并强调了使用这种方法来理解恒星结构的好处。