Quantum Emission from Two-Dimensional Black Holes

TL;DR

This paper analyzes Hawking radiation from two-dimensional dilatonic black holes, deriving the thermal spectrum and density matrix, and discusses backreaction effects and their implications for information loss.

Contribution

It provides an exact calculation of Hawking radiation and the density matrix for 2D black holes, including backreaction effects, using standard quantization and conformal anomaly techniques.

Findings

Hawking radiation is thermal with temperature λ/(2π).

The density matrix is shown to be purely thermal in the equilibrium regime.

Backreaction modifies the Bogoliubov transformation but does not restore information.

Abstract

We investigate Hawking radiation from two-dimensional dilatonic black holes using standard quantization techniques. In the background of a collapsing black hole solution the Bogoliubov coefficients can be exactly determined. In the regime after the black hole has settled down to an `equilibrium' state but before the backreaction becomes important these give the known result of a thermal distribution of Hawking radiation at temperature lambda/(2pi). The density matrix is computed in this regime and shown to be purely thermal. Similar techniques can be used to derive the stress tensor. The resulting expression agrees with the derivation based on the conformal anomaly and can be used to incorporate the backreaction. Corrections to the thermal density matrix are also examined, and it is argued that to leading order in perturbation theory the effect of the backreaction is to modify the Bogoliubov transformation, but not in a way that restores information lost to the black holes.