Singularity attenuation with quantum-mechanically revisited metric tensor

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.