Singularity avoidance by collapsing shells in quantum gravity

TL;DR

This paper develops a quantum model of a collapsing shell in spherical symmetry that avoids classical singularities through a unitary quantum evolution, providing insights into quantum gravity and singularity resolution.

Contribution

It introduces a non-perturbative quantum framework for a thin shell in spherical symmetry, demonstrating singularity avoidance via unitarity.

Findings

Classical singularity is resolved in the quantum model.

The quantum theory is constructed with a well-defined unitary evolution.

The model provides a concrete example of singularity avoidance in quantum gravity.

Abstract

We discuss a model describing exactly a thin spherically symmetric shell of matter with zero rest mass. We derive the reduced formulation of this system in which the variables are embeddings, their conjugate momenta, and Dirac observables. A non-perturbative quantum theory of this model is then constructed, leading to a unitary dynamics. As a consequence of unitarity, the classical singularity is fully avoided in the quantum theory.