We develop the canonical ADM approach to 2+1 dimensional gravity in the presence of point particles. The instantaneous York gauge can be applied for open universes. 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.
ADM approach to 2+1 dimensional gravity coupled to particles / P. MENOTTI; D. SEMINARA. - In: ANNALS OF PHYSICS. - ISSN 0003-4916. - STAMPA. - 279:(2000), pp. 282-310. [10.1006/aphy.1999.5972]
ADM approach to 2+1 dimensional gravity coupled to particles
SEMINARA, DOMENICO
2000
Abstract
We develop the canonical ADM approach to 2+1 dimensional gravity in the presence of point particles. The instantaneous York gauge can be applied for open universes. 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.
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