Quantum Probes of Timelike Naked Singularities in 2+1-Dimensional Power-Law Spacetimes

Abstract

The formation of naked singularities in 2 + 1-dimensional power-law spacetimes in linear Einstein-Maxwell and Einstein-scalar theories sourced by azimuthally symmetric electric field and a self-interacting real scalar field, respectively, are considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon and Dirac equations are used to probe the classical timelike naked singularities developed at r = 0. We show that when the classically singular spacetimes probed with scalar waves, the considered spacetimes remain singular. However, the spinorial wave probe of the singularity in the metric of a self-interacting real scalar field remains quantum regular. The notable outcome in this study is that the quantum regularity/singularity cannot be associated with the energy conditions.