Quantum probes of timelike naked singularities in the weak field regime of f (R) global monopole spacetime

Abstract

The formation of a naked singularity in f (R) global monopole spacetime is considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell equations are used to probe the classical timelike naked singularity developed at r = 0. We prove that the spatial derivative operator of the fields fails to be essentially self-adjoint. As a result, the classical timelike naked singularity formed in f (R) global monopole spacetime remains quantum mechanically singular when it is probed with quantum fields having different spin structures. Pitelli and Letelier (Phys. Rev. D 80 (2009) 104035) had shown that for quantum scalar (spin 0) probes the general relativistic global monopole singularity remains intact. For specific modes electromagnetic (spin 1) and Dirac field (spin 1/2) probes, however, we show that the global monopole spacetime behaves quantum mechanically regular. The admissibility of this singularity is also incorporated within the Gubser's singularity conjecture.

Quantum probe of Hořava-Lifshitz gravity

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

“…To probe the singularity with quantum wave packets/particles, we use the HM prescription which incorporates with the propagation of a scalar field in the background of a classically singular space-time. The brief review of this prescription is as follows (See references [15][16][17][18][19] for a detailed mathematical background ). The massive Klein -Gordon equation is the governing equation for the scalar field and can be written by splitting temporal and spatial parts as…”

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