(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame

TL;DR

This paper formulates the Hamiltonian dynamics of a two-particle system in (2+1)-dimensional Einstein gravity, revealing a phase space structure similar to Newtonian mechanics and discussing potential quantization approaches.

Contribution

It introduces a canonical phase space framework for the Einstein-Kepler problem in (2+1) dimensions, bridging relativistic gravity and Newtonian analogies.

Findings

Reduced phase space has dimension four with topology R^3 x S^1

Canonical chart explicitly shows Newtonian limit

Discussion on prospects for quantization

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.