Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity

TL;DR

This paper explores how loop quantum gravity affects the classical collapse of Lemaitre-Tolman-Bondi models, revealing that quantum effects do not fully resolve singularities but influence their nature and the structure of solutions.

Contribution

It provides an effective, anomaly-free quantum dynamics framework for LTB collapse models, analyzing singularity behavior and the impact of inhomogeneity in loop quantum gravity.

Findings

Classical singularities are not resolved by quantum corrections in the effective models.

Collapse may lead to shell-crossing singularities before central singularities.

Homogeneous solutions are obstructed, emphasizing the importance of inhomogeneous analysis.

Abstract

Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in addition to spherical symmetry turn out to take a simple form at the kinematical level of loop quantum gravity, which allows a discussion of their implications at the quantum level. Moreover, the spherically symmetric setting of inhomogeneity illustrates several non-trivial properties of lattice refinements of discrete quantum gravity. Nevertheless, the situation at the dynamical level is quite non-trivial and thus provides insights to the anomaly problem. At an effective level, consistent versions of the dynamics are presented which implement the conditions together with the dynamical constraints of gravity in an anomaly-free manner. These are then used for analytical as well as numerical investigations of the fate of classical singularities, including non-spacelike ones, as they generically develop in these models. None of the corrections used here resolve those singularities by regular effective geometries. However, there are numerical indications that the collapse ends in a tamer shell-crossing singularity prior to the formation of central singularities for mass functions giving a regular conserved mass density. Moreover, we find quantum gravitational obstructions to the existence of exactly homogeneous solutions within this class of models. This indicates that homogeneous models must be seen in a wider context of inhomogeneous solutions and their reduction in order to provide reliable dynamical conclusions.