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

2008/06/16 by Martin Bojowald, Tomohiro Harada, Rakesh Tibrewala · 4 citations
Mathematics · Medicine · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Classical mechanics #General relativity #Geometry #Gravitation #Gravitational collapse #Gravitational singularity #Loop quantum cosmology #Loop quantum gravity #Mathematics #Neuroblastoma Research and Treatments #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum gravity #Quantum mechanics #Singularity #Theoretical physics #gr-qc

paper · pdf · doi:10.1103/physrevd.78.064057

published as Phys.Rev.D78:064057,2008 · 56 pages, 42 figures

arxiv created 2008/06/16 · openalex publication_date 2008/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 nontrivial properties of lattice refinements of discrete quantum gravity. Nevertheless, the situation at the dynamical level is quite nontrivial 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 nonspacelike 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.

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Cited by

• Quantum induced shock dynamics in gravitational collapse: insights from effective models and numerical frameworks
• Radial asymptotics of Lemaître–Tolman–Bondi dust models
• Asymmetric Quantum Oppenheimer-Snyder Collapse
• A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model