Analysis of Two-Particle Systems in 2 + 1 Gravity Through Hamiltonian Dynamics

TL;DR

This paper investigates the Hamiltonian dynamics of two particles coupled to gravity in (2+1) dimensions, deriving general and quasi-static limit Hamiltonians and analyzing non-linear effects up to second order.

Contribution

It provides the first derivation of the general Hamiltonian for N-body systems in (2+1) gravity and explores non-linear dynamics in two-particle systems.

Findings

Derived the general Hamiltonian for N-body systems in (2+1) gravity

Analyzed non-linear terms up to second order in the coupling constant

Obtained exact Hamiltonian expressions in the quasi-static limit

Abstract

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.