Quantum Singularities in Static Spacetimes

TL;DR

This paper reviews the mathematical framework for understanding quantum singularities in static spacetimes, analyzing classical singularities with quantum wave equations, and identifying conditions under which quantum mechanics resolves or preserves these singularities.

Contribution

It provides a comprehensive review of quantum singularities in static spacetimes, including examples, analysis of wave equations, and criteria for self-adjointness to determine the quantum nature of singularities.

Findings

Quantum particles can exclude some classical singularities.

Certain singularities remain unresolved in quantum mechanics.

Boundary conditions are crucial for defining self-adjoint wave operators.

Abstract

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein-Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator into self-adjoint and emphasize their importance to the interpretation of quantum singularities.