Soft singularity and the fundamental length

TL;DR

The paper explores how certain 5D Kaluza-Klein solutions exhibit soft singularities near the Planck scale, suggesting these may be easier to resolve with quantum gravity than traditional hard singularities.

Contribution

It introduces the concept that soft singularities in higher-dimensional gravity could be more manageable in quantum gravity frameworks than hard singularities.

Findings

Kretschmann invariant reaches a maximum near the Planck scale.

Soft singularities may be easier to resolve in quantum gravity.

Application to avoiding hard singularities with gauge charges.

Abstract

It is shown that some regular solutions in 5D Kaluza-Klein gravity may have interesting properties if one from the parameters is in the Planck region. In this case the Kretschman metric invariant runs up to a maximal reachable value in nature, i.e. practically the metric becomes singular. This observation allows us to suppose that in this situation the problems with such soft singularity will be much easier resolved in the future quantum gravity then by the situation with the ordinary hard singularity (Reissner-Nordstr\"om singularity, for example). It is supposed that the analogous consideration can be applied for the avoiding the hard singularities connected with the gauge charges.