Quantum singularities in a model of f(R) Gravity

TL;DR

This paper investigates whether quantum fields can resolve classical naked singularities in a specific f(R) gravity model, finding that the singularity remains quantum mechanically problematic across different field types.

Contribution

It demonstrates that classical timelike naked singularities in this f(R) gravity model are not smoothed out by quantum effects, as the relevant operators are not essentially self-adjoint.

Findings

Quantum test fields do not resolve the naked singularity.

The spatial derivative operator is not essentially self-adjoint.

The singularity remains quantum mechanically singular.

Abstract

The formation of a naked singularity in a model of f(R) gravity having as source a linear electromagnetic field 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 remains quantum mechanically singular when it is probed with quantum fields having different spin structures.