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arXiv · hep-th/9810073

Integrability of the N-body problem in (2+1)-AdS gravity

P. Valtancoli
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Abstract

We derive a first order formalism for solving the scattering of point sources in (2+1) gravity with negative cosmological constant. We show that their physical motion can be mapped, with a polydromic coordinate transformation, to a trivial motion, in such a way that the point sources move as time-like geodesics (in the case of particles) or as space-like geodesics (in the case of BTZ black holes) of a three-dimensional hypersurface immersed in a four-dimensional Minkowskian space-time, and that the two-body dynamics is solved by two invariant masses, whose difference is simply related to the total angular momentum of the system.

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P. Valtancoli. 1998-10-12. Integrability of the N-body problem in (2+1)-AdS gravity. https://doi.org/10.1142/s0217751x00002214

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