Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space

TL;DR

This paper explores how loop quantum gravity modifies the gravitational collapse of a dust cloud, showing that quantum effects replace singularities with bounces and lead to cyclic or bounded collapse scenarios.

Contribution

It demonstrates that the effective dynamics of dust collapse in LQG reduces to loop quantum cosmology, revealing quantum geometric effects on gravitational collapse and singularity resolution.

Findings

Singularity is replaced by a bounce in both collapse cases.

Dust cloud undergoes cyclic contraction and expansion in the bound case.

A mass threshold for trapped surface formation is identified.

Abstract

Based on the effective dynamics in the $\bar \mu$ scheme of the spherical symmetry reduced model in the reduced phase space formulation of loop quantum gravity (LQG), we investigate the gravitational collapse of a homogeneous dust cloud, with Gaussian dust serving as both the reference field and the source of the gravitational collapse. The effective dynamics from the considered model for a homogeneous dust cloud reduces precisely to the effective dynamics of loop quantum cosmology (LQC) with extrinsic curvature based K-quantization, indicating that the LQC effective dynamics lives as a subsector of the model presented here. In both the marginally bound and the bound cases of the collapse in effective dynamics, the singularity is resolved and replaced by a bounce. Though quantum geometric modification from spatial curvature is not directly included in the K-quantization it does affect the qualitative dynamics of the collapsing dust cloud in the sense that on the one hand for the marginally bound case, the dust cloud bounces once at fixed maximum energy density and on the other hand for the bound case, the dust cloud undergoes infinite cycles of contraction and expansion at energy densities dependent on the dust mass. Finally, the mass threshold for the formation of a trapped surface in each case is found and the matching conditions between the interior collapsing spacetime and an effective exterior static solution are discussed.