CLASSICAL AND QUANTUM GEOMETRODYNAMICS OF 2-DIMENSIONAL VACUUM DILATONIC BLACK-HOLES

We perform a canonical analysis of the system of two-dimensional (2D) vacuum dilatonic black holes. Our basic variables are closely tied to the spacetime geometry and we do not make the field redefinitions whic h have been made by other authors. We present a careful discussion of asymptotics in this canonical formalism. Canonical transformations are made to variables which (on shell) have a clear spacetime significanc e. We are able to deduce the location of the horizon on the spatial sl ice (on shell) from the vanishing of a combination of canonical data. The constraints dramatically simplify in terms of the new canonical va riables and quantization is easy. The physical interpretation of the v ariable conjugate;ate to the Arnowitt-Deser-Misner mass is clarified. This work closely parallels that done by Kuchar for the vacuum Schwarz schild black holes and is a starting point for a similar analysis, now in progress, for the case of a massless scalar field conformally coup led to a 2D dilatonic black hole.