Physical singularity in the regular spacetime and fundamental length

TL;DR

This paper demonstrates that regular solutions in 5D Kaluza-Klein gravity exhibit singularities due to a fundamental minimal length, linking geometric properties to quantum-scale phenomena and resulting in a singular Ricci scalar.

Contribution

It reveals that regular 5D Kaluza-Klein solutions inherently contain singularities connected to the existence of a minimal length in nature.

Findings

Derivative of $G_{55}$ leads to Dirac delta function

Ricci scalar becomes singular due to squared derivative

Regular solutions in 5D gravity are not free of singularities

Abstract

It is shown that formally regular solutions in 5D Kaluza-Klein gravity have singularities. This phenomenon is connected with the existence of a minimal length in nature. The calculation of the derivative of the $G_{55}$ metric component leads to the appearance of the Dirac's $\delta-$function. In this case the Ricci scalar becomes singular since there is a square of this derivative.