Canonical Quantization of Spherically Symmetric Dust Collapse

TL;DR

This paper presents a canonical quantization of spherical dust collapse models, deriving exact solutions that describe Hawking radiation and black hole entropy, advancing understanding of quantum effects in gravitational collapse.

Contribution

It introduces an exact solution to the Wheeler-DeWitt equation for inhomogeneous dust collapse, linking quantum gravity effects to black hole thermodynamics.

Findings

Solutions describe Hawking radiation.

Provides a microcanonical description of black hole entropy.

Raises questions about gravity's fundamental degrees of freedom.

Abstract

Quantum gravity effects are likely to play a crucial role in determining the outcome of gravitational collapse during its final stages. In this contribution we will outline a canonical quantization of the LeMaitre-Tolman-Bondi models, which describe the collapse of spherical, inhomogeneous, non-rotating dust. Although there are many models of gravitational collapse, this particular class of models stands out for its simplicity and the fact that both black holes and naked singularity end states may be realized on the classical level, depending on the initial conditions. We will obtain the appropriate Wheeler-DeWitt equation and then solve it exactly, after regularization on a spatial lattice. The solutions describe Hawking radiation and provide an elegant microcanonical description of black hole entropy, but they raise other questions, most importantly concerning the nature of gravity's fundamental degrees of freedom.