Quantum singularity of Levi-Civita spacetimes

TL;DR

This paper investigates the quantum nature of singularities in Levi-Civita spacetimes by applying Weyl's criterion to determine if the wave operator is essentially self-adjoint, revealing quantum properties linked to spacetime metrics.

Contribution

It introduces a method using Weyl's limit point-limit circle criterion to analyze quantum singularities in Levi-Civita spacetimes, connecting quantum behavior with metric parameters.

Findings

Quantum singularities depend on metric parameters.

Weyl's criterion effectively classifies quantum singularities.

Scalar wave packets reveal physical properties of the spacetime.

Abstract

Quantum singularities in general relativistic spacetimes are determined by the behavior of quantum test particles. A static spacetime is quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint. Here Weyl's limit point-limit circle criterion is used to determine whether a wave operator is essentially self-adjoint. This test is then applied to scalar wave packets in Levi-Civita spacetimes to help elucidate the physical properties of the spacetimes in terms of their metric parameters.