Quantum singularities in conformally static spacetimes

TL;DR

This paper extends the concept of quantum singularities to conformally static spacetimes and investigates their presence in specific cosmological and spacetime models, revealing conditions under which classical singularities are quantum mechanically detectable.

Contribution

It introduces an extension of quantum singularity analysis to conformally static spacetimes and applies it to test cases, showing how coupling affects quantum singularity detection.

Findings

Classical singularities in FRW universe with a cosmic string are quantum mechanically singular.

In Roberts spacetime, non-minimally coupled scalar waves with ξ ≥ 2 do not detect the singularity.

Quantum singularity detection depends on the scalar wave coupling constant.

Abstract

After a brief review of the standard definition and analysis of classical singularities in general relativistic spacetimes, and of quantum singularities in static spacetimes with timelike classical singularities, an extension of quantum singularities to conformally static spacetimes is summarized and applied to two test cases. The timelike classical singularities in a Friedmann-Robertson-Walker (FRW) universe with a cosmic string, and in Roberts spacetime, are shown to be quantum mechanically singular when tested by either minimally coupled or conformally coupled scalar waves. In the Roberts case, however, non-minimally coupled scalar waves with a coupling constant $\xi \ge 2$ do not detect the classical singularity.