Probing naked singularities in the charged and uncharged $\gamma$-metrics with quantum wave packets

TL;DR

This paper investigates whether quantum wave packets can resolve naked singularities in charged and uncharged Zipoy-Voorhees spacetimes, finding that most singularities remain quantum mechanically problematic except for specific modes and parameters.

Contribution

It provides a detailed quantum analysis of naked singularities in Zipoy-Voorhees spacetimes, revealing conditions under which they are partially healed or remain singular.

Findings

Outer singularities are quantum mechanically singular for all parameters.

Directional singularities on the axis are partially healed for specific modes and parameters.

Allowing all modes, singularities remain quantum mechanically problematic.

Abstract

The non-trivial naked singularities that possess directional behavior in the charged and uncharged Zipoy-Voorhees (ZV) spacetimes, known as {\gamma} - metrics are investigated within the context of quantum mechanics. Classically singular spacetime is understood as a geodesic incompleteness with respect to a particle probe, while quantum singularity is understood as a non-unique evolution of test quantum wave packets. In this study, quantum wave packets obeying Klein - Gordon equation are used to probe timelike naked singularities. It is shown by rigorous mathematical calculations that the outermost singularity developed in the charged and uncharged Zipoy-Voorhees spacetime on the equatorial plane is quantum mechanically singular for all values of the deformation parameter {\gamma}. However, directional singularities that develop on the symmetry axis is shown to be healed partially for specific range of the parameter {\gamma}, if the analysis is restricted purposely to only specific mode (s-wave mode). Allowing arbitrary modes, classical directional singularities remains quantum singular.