ADM approach to 2+1 dimensional gravity coupled to particles

摘要

We develop the canonical ABM 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 al ises in the ADM treatment by considering the lime development of the conformal factor at the locations where the extrinsic curvature tensor vanishes. (C) 2000 Academic Press, Inc. [References: 37]