Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions

Details Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions

2007-10-11

arxiv.org/abs/0710.2164v1

Phys.Rev.D76:124021,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, no figures

Scientific paper

10.1103/PhysRevD.76.124021

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 $T_{\mathrm H}=\hbar\sqrt{G\Lambda M}/2\pi$, 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.

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