Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes

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.

21 pages, latex file

References in corpus (3)

• Evanescent Black Holes
• Geometrodynamics of Schwarzschild Black Holes
• Hamiltonian Approach to 2D Dilaton-Gravities and Invariant Adm Mass

Cited by in corpus (16)

• Dilaton Gravity in Two Dimensions
• Hamiltonian thermodynamics of the Reissner-Nordström-anti-de Sitter black hole
• Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
• Quantization of Midisuperspace Models
• Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
• Hamiltonian thermodynamics of a Lovelock black hole
• On the Canonical Reduction of Spherically Symmetric Gravity
• Geometrodynamical Formulation of Two-Dimensional Dilaton Gravity
• Boundary Conditions and Quasilocal Energy in the Canonical Formulation of All 1+1 Models of Gravity
• Hamiltonian thermodynamics of two-dimensional vacuum dilatonic black holes
• Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model
• Quantum gravity corrections to the Schwarzschild mass
• Polymer quantization of CGHS model- I
• Transgressing the horizons: Time operator in two-dimensional dilaton gravity
• Quantum fluctuating geometries and the information paradox
• Quantum fluctuating CGHS geometries and the information paradox