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 ($% spin$ $1/2$) 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.