Canonical Quantization of Spherically Symmetric Dust Collapse

Abstract

Quantum gravity effects are likely to play a crucial role in determining the outcome of gravitational collapse during its final stages. In this contribution we will outline a canonical quantization of the LeMaitre-Tolman-Bondi models, which describe the collapse of spherical, inhomogeneous, non-rotating dust. Although there are many models of gravitational collapse, this particular class of models stands out for its simplicity and the fact that both black holes and naked singularity end states may be realized on the classical level, depending on the initial conditions. We will obtain the appropriate Wheeler-DeWitt equation and then solve it exactly, after regularization on a spatial lattice. The solutions describe Hawking radiation and provide an elegant microcanonical description of black hole entropy, but they raise other questions, most importantly concerning the nature of gravity's fundamental degrees of freedom.

19 pages no figures. Contribution to a festschrift in honor of Joshua N. Goldberg

References in corpus (7)

• Hawking radiation from the quantum Lemaitre-Tolman-Bondi model
• Mass Spectrum and Statistical Entropy of the BTZ black hole from Canonical Quantum Gravity
• Gibbs' paradox and black-hole entropy
• Spectrum and Statistical Entropy of AdS Black Holes
• Classical and Quantum Gravitational Collapse in d-dim AdS Spacetime II. Quantum States and Hawking Radiation
• Quantum Gravitational Collapse in the Lemaitre-Tolman-Bondi Model with a Positive Cosmological Constant
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Cited by in corpus (6)

• Quantum gravity of dust collapse: shock waves from black holes
• On the fate of quantum black holes
• Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations
• General relativity in the radial gauge: Reduced phase space and canonical structure
• Quantum dust cores of black holes
• Infrared signatures of quantum bounce in a minisuperspace analysis of Lema\^ıtre-Tolman-Bondi dust collapse