Generalized analysis of a dust collapse in effective loop quantum gravity: fate of shocks and covariance

TL;DR

This paper develops a systematic framework for effective spherically symmetric models in loop quantum gravity, ensuring covariance and consistency, and demonstrates the resolution of singularities without shocks in dust collapse scenarios.

Contribution

It introduces a generalized method to construct covariant LQG-inspired models, addressing previous issues with shocks and covariance in phenomenological approaches.

Findings

Models resolve singularities via quantum bounce effects.

Shock solutions are absent even after coordinate transformations.

The approach emphasizes the importance of the determinant of the triad, not the metric.

Abstract

Based on modifications inspired from loop quantum gravity (LQG), spherically symmetric models have recently been explored to understand the resolution of classical singularities and the fate of the spacetime beyond. While such phenomenological studies have provided useful insights, questions remain on whether such models exhibit some of the desired properties such as consistent LTB conditions, covariance and compatibility with the improved dynamics of loop quantum cosmology in the cosmological and LTB sectors. We provide a systematic procedure to construct effective spherically symmetric models encoding LQG modifications as a $1+1$ field theory models encoding these properties following the analysis in our companion paper. As concrete examples of our generalized strategy we obtain and compare with different phenomenological models which have been investigated recently and demonstrate resolution of singularity by quantum geometry effects via a bounce. These include models with areal gauge fixing, a polymerized vacuum solution, polymerized junction conditions and an Oppenheimer-Snyder dust collapse model. An important insight from our approach is that the dynamical equations care about the $\det(e)$ part rather than the square root of the determinant of the spatial metric. As a result, shock solutions which have been argued to exist in some models are found to be absent even if one considers coordinate transformations.