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.