Canonical Quantization of Spherically Symmetric Dust Collapse

Details Canonical Quantization of Spherically Symmetric Dust Collapse Canonical Quantization of Spherically Symmetric Dust Collapse

2011-11-29

arxiv.org/abs/1111.6821v1

Gen.Rel.Grav.43:3429,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1007/s10714-011-1240-4

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.

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