On the Canonical Reduction of Spherically Symmetric Gravity

Abstract

In a thorough paper Kuchar has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) spherically symmetric general relativity. The essential technical ingredient in Kuchar's analysis is a canonical transformation to a certain chart on the gravitational phase space which features the Schwarzschild mass parameter $M_S$, expressed in terms of what are essentially Arnowitt-Deser-Misner variables, as a canonical coordinate. In this paper we discuss the geometric interpretation of Kuchar's canonical transformation in terms of the theory of quasilocal energy-momentum in general relativity given by Brown and York. We find Kuchar's transformation to be a ``sphere-dependent boost to the rest frame," where the ``rest frame'' is defined by vanishing quasilocal momentum. Furthermore, our formalism is general enough to cover the case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing Kuchař's original work for Schwarzschild black holes from the framework of hyperbolic geometry, we present new results concerning the canonical reduction of Witten-black-hole geometrodynamics.

Revtex, 35 pages, no figures

References in corpus (12)

• Geometrodynamics of Schwarzschild Black Holes
• Poisson Structure Induced (Topological) Field Theories
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Spherically Symmetric Gravity as a Completely Integrable System
• Hamiltonian thermodynamics of the Schwarzschild black hole
• The Black Holes of a General Two-Dimensional Dilaton Gravity Theory
• Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions
• Dirac Quantization Gravity-Yang-Mills Systems in 1+1 Dimensions
• Poisson-Sigma-Models: A Generalization of 2-D Gravity Yang-Mills-Systems
• The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant
• Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes
• Consequence of Hawking radiation from 2d dilaton black holes

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• Hamiltonian spacetime dynamics with a spherical null-dust shell
• Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
• Integrating Geometry in General 2D Dilaton Gravity with Matter
• Hamiltonian thermodynamics of a Lovelock black hole
• Effective action and Hawking radiation for dilaton coupled scalars in two dimensions
• Hawking radiation and masses in generalized dilaton theories
• Nonperturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter
• Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories
• Absolute conservation law for black holes
• Hamiltonian thermodynamics of two-dimensional vacuum dilatonic black holes
• Long time black hole evaporation with bounded Hawking flux
• Boundary Conditions and Quasilocal Energy in the Canonical Formulation of All 1+1 Models of Gravity
• Two-Dilaton Theories in Two Dimensions from Dimensional Reduction
• Universal flow equations and chaos bound saturation in 2d dilaton gravity
• On static solutions in 2D dilaton gravity with scalar matter
• Physics-to-gauge conversion at black hole horizons
• Deformations of the Schwarzschild Black Hole
• Entanglement of quantum fields via classical gravity
• Hamiltonians for a general dilaton gravity theory on a spacetime with a non-orthogonal, timelike or spacelike outer boundary
• Ghost-free infinite-derivative dilaton gravity in two dimensions