Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions

Abstract

We develop the canonical theory of gravitational collapse in 2+1 dimensions with a negative cosmological constant and obtain exact solutions of the Wheeler--DeWitt equation regularized on a lattice. We employ these solutions to derive the Hawking radiation from black holes formed in all models of dust collapse. We obtain an (approximate) Planck spectrum near the horizon characterized by the Hawking temperature $T_{\mathrm{H}}=\hslash \sqrt{G\Lambda M}/2\pi$, where $M$ is the mass of a black hole that is presumed to form at the center of the collapsing matter cloud and $-\Lambda$ is the cosmological constant. Our solutions to the Wheeler-DeWitt equation are exact, so we are able to reliably compute the greybody factors that result from going beyond the near horizon region.

27 pages, no figures

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• Mass Spectrum and Statistical Entropy of the BTZ black hole from Canonical Quantum Gravity
• The Role of Angular Momentum and Cosmic Censorship in the (2+1)-Dimensional Rotating Shell Collapse
• A quantum peek inside the black hole event horizon
• Indefinite oscillators and black-hole evaporation
• Dynamical formation and evolution of (2+1)-dimensional charged black holes
• Classical and Quantum Gravitational Collapse in d-dim AdS Spacetime I. Classical Solutions
• Classical and Quantum Gravitational Collapse in d-dim AdS Spacetime II. Quantum States and Hawking Radiation
• Tunneling during Quantum Collapse in AdS Spacetime
• Quantum Gravitational Collapse in the Lemaitre-Tolman-Bondi Model with a Positive Cosmological Constant
• A Rotating, Inhomogeneous Dust Interior for the BTZ Black Hole
• Canonical Partition function of Loop Black Holes
• Infrared signatures of quantum bounce in a minisuperspace analysis of Lema\^ıtre-Tolman-Bondi dust collapse
• Quantum dust collapse in 2+1 dimensions
• Schwarzschild-de Sitter black hole in canonical quantization
• Bose Condensation and the BTZ Black Hole
• Canonical Chern-Simons Gravity