A loop quantization of the marginally bound Lema\^itre-Tolman-Bondi dust model

TL;DR

This paper develops a loop quantum gravity model for the Lemaître-Tolman-Bondi dust collapse, showing that quantum effects resolve classical singularities through a bounce and analyzing the accuracy of effective theories.

Contribution

It introduces a full quantum LTB model as non-interacting shells with non-singular evolution, and compares loop quantum gravity with Wheeler-DeWitt quantization.

Findings

Wave packets bounce at Planckian densities avoiding singularities

Effective theory accuracy decreases near the bounce due to interference patterns

Quantum dynamics differ from classical collapse, indicating singularity resolution

Abstract

We present a loop quantization of the marginally bound Lema\^itre-Tolman-Bondi (LTB) model, describing the gravitational collapse of pressureless dust in spherical symmetry. The full quantum LTB model is constructed as a collection of non-interacting shells, each governed by an individual single-shell loop quantum dynamics. We show that the single-shell evolution is non-singular and that wave packets initially peaked on a collapsing trajectory undergo a bounce at Planckian energy densities and subsequently follow an expanding classical trajectory, resolving the classical central curvature singularity. We also compare the loop quantum theory with the Wheeler-DeWitt quantization of the same model and assess the accuracy of the loop quantum gravity effective theory in reproducing the full quantum dynamics. Specifically, we find that initially collapsing wave packets generically develop an interference pattern at the bounce, which suppresses the accuracy of the effective theory near the center of the dust cloud.