Quantum Probe of Time-like Naked Singularities for Electrically and Magnetically Charged Black Holes in a Model of Nonlinear Electrodynamics

TL;DR

This paper investigates the quantum behavior of time-like naked singularities in charged black holes within a nonlinear electrodynamics model, demonstrating that quantum mechanics can render these singularities effectively regular.

Contribution

It provides a detailed quantum analysis showing that certain naked singularities become quantum regular, with unique wave evolution, in a specific nonlinear electrodynamics framework.

Findings

Quantum wave operators are essentially self-adjoint at singularities.

Unique quantum evolution is mode-dependent for different black hole charges.

Electrically charged case restricts evolution to s-wave mode.

Abstract

The time-like naked singularities of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov is investigated within the framework of quantum mechanics. In view of quantum mechanics, the space-time is quantum regular provided that the time evolution of the test quantum wave packet uniquely propagates on an underlying background. Rigorous calculations have shown that when the singularity is probed with specific quantum wave/particle modes, the quantum wave operator turns out to be essentially self-adjoint. Thus, the time evolution of the quantum wave/particle is determined uniquely. In the case of electrically charged black hole background, the unique evolution is restricted to s-wave only. For the two different magnetically charged black hole backgrounds, the time evolution is restricted to different modes for each case.