Analysis of two-particle systems in 2 + 1 gravity through Hamiltonian dynamics

We study the dynamics of particles coupled to gravity in (2 + 1) dimensions. Using the ADM formalism, we derive the general Hamiltonian for an N-body system and analyze the dynamics of a two-particle system. Nonlinear terms are found up to second order in κ in the general case, and to every order in the quasi-static limit.