Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes

TL;DR

This paper performs a canonical analysis of 2D vacuum dilatonic black holes, clarifying the geometric significance of variables, simplifying constraints, and paving the way for quantum analysis and extensions to scalar field couplings.

Contribution

It introduces a novel canonical formalism for 2D dilatonic black holes without field redefinitions, enabling easier quantization and geometric interpretation.

Findings

Canonical variables linked to spacetime geometry identified

Horizon location deduced from canonical data

Simplified constraints facilitate quantization

Abstract

We perform a canonical analysis of the system of 2d vacuum dilatonic black holes. Our basic variables are closely tied to the spacetime geometry and we do not make the field redefinitions which have been made by other authors. We present a careful discssion of asymptotics in this canonical formalism. Canonical transformations are made to variables which (on shell) have a clear spacetime significance. We are able to deduce the location of the horizon on the spatial slice (on shell) from the vanishing of a combination of canonical data. The constraints dramatically simplify in terms of the new canonical variables and quantization is easy. The physical interpretation of the variable conjugate to the ADM mass is clarified. This work closely parallels that done by Kucha{\v r} for the vacuum Schwarzschild black holes and is a starting point for a similar analysis, now in progress, for the case of a massless scalar field conformally coupled to a 2d dilatonic black hole.