Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions

TL;DR

This paper develops a canonical quantum gravity framework for 2+1 dimensional gravitational collapse with a negative cosmological constant, deriving exact Wheeler-DeWitt solutions and analyzing Hawking radiation with greybody factors.

Contribution

It provides the first exact solutions to the Wheeler-DeWitt equation for 2+1D collapse and derives Hawking radiation spectra including greybody factors.

Findings

Exact Wheeler-DeWitt solutions for 2+1D collapse

Derivation of Hawking radiation with Planck spectrum

Calculation of greybody factors beyond near horizon approximation

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