ADM approach to 2+1 dimensional gravity coupled to particles

Abstract

We develop the canonical ADM approach to 2+1 dimensional gravity in presence of point particles. The instantaneous York gauge can be applied for open universes or universes with the topology of the sphere. The sequence of canonical ADM equations is solved in terms of the conformal factor. A simple derivation is given for the solution of the two body problem. A geometrical characterization is given for the apparent singularities occurring in the N-body problem and it is shown how the Garnier hamiltonian system arises in the ADM treatment by considering the time development of the conformal factor at the locations where the extrinsic curvature tensor vanishes.

34 pages, LaTex

References in corpus (8)

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• The 2+1 Kepler Problem and Its Quantization
• Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles
• Point massive particle in General Relativity
• The point-particle solution and the asymptotic flatness in 2+1 Horava gravity
• On the solution of Liouville equation
• Functional approach to 2+1 dimensional gravity coupled to particles
• Hamiltonian solutions of the 3-body problem in (2+1)-gravity
• The diagonal two-point correlations of the Ising model on the anisotropic triangular lattice and Garnier systems
• A Quantization of 2+1-Gravity Related to High-Energy Yang-Mills Theory