Quantum Imploding Scalar Fields

TL;DR

This paper investigates how quantum gravity affects the formation of singularities caused by scalar fields, finding that quantum effects can regularize the wavefunction at the origin, potentially avoiding classical singularities.

Contribution

It introduces two minispace Hamiltonian models in canonical quantum gravity to analyze scalar field singularities and shows quantum effects can make the wavefunction finite at the origin.

Findings

Quantum wavefunction remains finite at the origin.

Quantum effects may prevent classical singularity formation.

Models suggest regularization of scalar field singularities in quantum gravity.

Abstract

The d'Alembertian $\Box\phi=0$ has solution $\phi=f(v)/r$, where $f$ is a function of a null coordinate $v$, and this allows creation of a divergent singularity out of nothing. In scalar-Einstein theory a similar situation arises both for the scalar field and also for curvature invariants such as the Ricci scalar. Here what happens in canonical quantum gravity is investigated. Two minispace Hamiltonian systems are set up: extrapolation and approximation of these indicates that the quantum mechanical wavefunction can be finite at the origin.