(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame
Abstract
We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but possibly spinning particle. The reduced phase space \Gamma_{red} has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the phase space of a Newtonian two-body system in the centre-of-mass frame, and we find on \Gamma_{red} a canonical chart that makes this analogue explicit and reduces to the Newtonian chart in the appropriate limit. Prospects for quantization are commented on.
Cite
@article{arxiv.gr-qc/9908025,
title = {(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame},
author = {Jorma Louko and Hans-Juergen Matschull},
journal= {arXiv preprint arXiv:gr-qc/9908025},
year = {2009}
}
Comments
38 pages, REVTeX v3.1 with amsfonts and epsf, 12 eps figures. (v2: Presentational improvement, references added, typos corrected.)