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. Non-linear terms are found up to second-order order in {\kappa} in the general case, and to every order in the quasi-static limit.