The space and initial singularities are reexamined in the most reliable solutions to the Einstein's field equations (EFE), that is, the Einstein–Gilbert–Straus (EGS) metric. In discretized Finsler geometry, additional curvatures and thereby geometric structures likely emerge, which are distinct from the conventional spacetime curvatures and geometric structures that the Einstein's theory of general relativity introduced. The generalized fundamental tensor, which is obtained in the Fisleriean geometry, imposes quantum-mechanically revisions on the Landau–Raychaudhuri evolution equations. The time-like geodesic congruence in EGS metric is then analyzed, analytically and numerically. The evolution of a family of trajectories whose congruence is defined by the flow lines generated by velocity fields is determined. We conclude that both two types of singularities seem to be attenuated or even regulate. With the singularity attenuation, we refer to the fundamental nature of the additional curvatures at quantum relativistic scales.

中文翻译：

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用量子力学重新审视度量张量的奇异性衰减

空间和初始奇点在爱因斯坦场方程（EFE）最可靠的解中被重新检验，即爱因斯坦-吉尔伯特-斯特劳斯（EGS）度量。在离散芬斯勒几何中，可能会出现额外的曲率和几何结构，这与爱因斯坦广义相对论引入的传统时空曲率和几何结构不同。在费斯勒几何中获得的广义基本张量对朗道-雷乔杜里演化方程进行了量子力学修正。然后对 EGS 度量中的类时间测地线同余进行分析和数值分析。确定了一系列轨迹的演化，这些轨迹的一致性由速度场生成的流线定义。我们得出的结论是，两种类型的奇点似乎都被削弱甚至受到调节。对于奇点衰减，我们指的是量子相对论尺度上附加曲率的基本性质。