In the context of modified $f( \mathcal{G} )$ gravity, we study the appearance of anisotropic compact stellar objects. The space–time geometry is characterized by the metric potentials, and to solve the field equations, we consider their specific form known as the Tolman–Kuchowicz space–time. The obtained solutions are free of singularities and satisfy all requirements for stellar objects. We consider the observational data for models of the stars Cen X-3, EXO 1785-248, and LMC X-4, and taking these data into account, we obtain the values of the physical parameters from the matching conditions for the interior Tolman–Kuchowicz space–time and the exterior Schwarzschild metric. In addition, we discuss some physical attributes of anisotropic compact stellar structures to verify the physical validity and stability of the proposed model. We perform a three-dimensional graphical analysis that allows obtaining a representation of the physical behavior of these compact objects. We note that all three compact objects correspond to physically accepted models.

中文翻译：

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$$f(\mathcal{G})$$引力中恒星结构的动力学行为

在修正的 $f(\mathcal{G})$ 引力的背景下，我们研究了各向异性致密恒星物体的外观。时空几何以度量势为特征，为了求解场方程，我们考虑它们的特定形式，称为 Tolman-Kuchowicz 时空。得到的解没有奇点，满足对恒星物体的所有要求。我们考虑了恒星 Cen X-3、EXO 1785-248 和 LMC X-4 模型的观测数据，并考虑到这些数据，我们从内部 Tolman-的匹配条件中获得了物理参数值。 Kuchowicz 时空和外部 Schwarzschild 度量。此外，我们讨论了各向异性致密恒星结构的一些物理属性，以验证所提出模型的物理有效性和稳定性。我们执行三维图形分析，可以获得这些紧凑物体的物理行为的表示。我们注意到所有三个紧凑对象都对应于物理上可接受的模型。