Probing naked singularities in the charged and uncharged $\gamma$-metrics with quantum wave packets
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.
Keywords
Cite
@article{arxiv.2307.08292,
title = {Probing naked singularities in the charged and uncharged $\gamma$-metrics with quantum wave packets},
author = {Ozay Gurtug and Mustafa Halilsoy and Mert Mangut},
journal= {arXiv preprint arXiv:2307.08292},
year = {2023}
}
Comments
Slightly detailed version