Pure quantum freezing of the 5$^{th}$ dimension

TL;DR

The paper proposes that quantum freezing of the fifth dimension in 5D Kaluza-Klein gravity prevents rapid metric signature changes at the Planck scale, avoiding singularities in extremal Reissner-Nordström solutions.

Contribution

It introduces the concept of pure quantum freezing of the fifth dimension to resolve signature change issues and eliminate singularities in 5D gravitational flux tube solutions.

Findings

Signature change region is approximately at the Planck length.

Quantum freezing prevents rapid metric signature transitions.

Singularity is avoided in the extended Reissner-Nordström metric.

Abstract

It is shown that superthin and superlong gravitational flux tube solutions in the 5D Kaluza-Klein gravity have the region $(\approx l_{Pl})$ where the metric signature changes from $\{+,-,-,-,- \}$ to $\{-,-,-,-,+ \}$. Such change is too quickly from one of the paradigms of quantum gravity which tells that the Planck length is the minimal length in the nature and consequently the physical quantities can not change very quickly in the course of this length. For avoiding such dynamic it is supposed that a pure quantum freezing of the dynamic of the $5^{th}$ dimension takes place. As the continuation of the flux tube metric in the longitudinal direction the Reissner-Nordstr\"om metric is proposed. In the consequence of such construction one can avoid the appearance of a point-like singularity in the extremal Reissner-Nordstr\"om solution.