Classical and quantum properties of a 2-sphere singularity

TL;DR

This paper investigates a two-sphere classical singularity in a specific spacetime metric, revealing its properties as both a weak gravitational and quantum singularity, with implications for classical and quantum gravity theories.

Contribution

It demonstrates that the two-sphere singularity is a scalar curvature singularity that is both timelike and gravitationally weak, and also quantum mechanically singular due to non-essential self-adjointness.

Findings

The singularity is a scalar curvature singularity.

It is timelike and gravitationally weak.

The Klein-Gordon operator is not essentially self-adjoint near the singularity.

Abstract

Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.