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arXiv · 2307.08292

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

Ozay Gurtug·Mustafa Halilsoy·Mert Mangut
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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.

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Ozay Gurtug, Mustafa Halilsoy, Mert Mangut. 2023-07-17. Probing naked singularities in the charged and uncharged $\gamma$-metrics with quantum wave packets. https://doi.org/10.1007/s10714-023-03146-z

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