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, 104035, 2009) 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 ( $1/2$) 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.

14 pages, 5 figures. Accepted for publication in JHEP. arXiv admin note: substantial text overlap with arXiv:1205.5125

References in corpus (5)

• Singularity Resolution in Loop Quantum Cosmology: A Brief Overview
• n-Dimensional FLRW Quantum Cosmology
• Quantum Singularities in Spacetimes with Spherical and Cylindrical Topological Defects
• Quantum singularities in a model of f(R) Gravity
• Classical and Quantum Singularities of Levi-Civita Spacetimes with and without a Positive Cosmological Constant

Cited by in corpus (9)

• The fragmentation instability of a black hole with $f(R)$ global monopole under GUP
• The neutrino pair annihilation ($\nu \bar{\nu }⟶e^{-}{e}^{+}$)around a massive source with an $f(R)$ global monopole
• Quantum probes of timelike naked singularities in $2+1-$ dimensional power - law spacetimes
• Quantum Probe of Hořava-Lifshitz Gravity
• Vacuum Fluctuations and Boundary Conditions in a Global Monopole
• Quantum Probe of Time-like Naked Singularities for Electrically and Magnetically Charged Black Holes in a Model of Nonlinear Electrodynamics
• Global Monopole metric in 2+1-dimensions
• Directional Quantum Singularities in Curzon Spacetime
• Crossing the singularity of a gravitational wave collision