Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-12-28
Nucl.Phys.Proc.Suppl. 88 (2000) 132-141
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, LaTeX, Contribution to "Constrained Dynamics and Quantum Gravity", Villasimius, Sept.13-17 1999
Scientific paper
10.1016/S0920-5632(00)00761-1
The canonical ADM equations are solved in terms of the conformal factor in the instantaneous York gauge. 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. The equations of motion for the position of the particles and of the apparent singularities and also the time dependence of the linear residues at such singularities are given by the transformation induced by an energy momentum tensor of a conformal Liouville theory. Such an equation encodes completely the dynamics of the system.
Menotti Pietro
Seminara Domenico
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