Quantum Gravity near Apparent Horizon and Two Dimensional Dilaton Gravity

TL;DR

This paper investigates Hawking radiation in two-dimensional dilaton black holes using quantum gravity near the apparent horizon, revealing mass-independent radiation and horizon dynamics, while constructing a canonical formalism and analyzing quantum properties.

Contribution

It develops a canonical formalism for 2D dilaton gravity and analyzes quantum effects near the horizon, providing new insights into black hole evaporation in this setting.

Findings

Hawking radiation mass loss rate is independent of black hole mass

Apparent horizon recedes to the singularity during evaporation

Quantum gravity can be constructed near curvature singularities

Abstract

We study the Hawking radiation in two dimensional dilaton black hole by means of quantum gravity holding near the apparent horizon. First of all, we construct the canonical formalism of the dilaton gravity in two dimensions. Then the Vaidya metric corresponding to the dilaton black hole is established where it is shown that the dilaton field takes a form of the linear dilaton. Based on the canonical formalism and the Vaidya metric, we proceed to analyze quantum properties of a dynamical black hole. It is found that the mass loss rate of the Hawking radiation is independent of the black hole mass and at the same time the apparent horizon recedes to the singularity as shown in other studies of two dimensional gravity. It is interesting that one can construct quantum gravity even near the curvature singularity and draw the same conclusion with respect to the Hawking radiation as the above-mentioned picture. Unfortunately, the present formalism seems to be ignorant of the contributions from the functional measures over the gravitational field, the dilaton and the ghosts.