Particles on a Circle in Canonical Lineal Gravity

Abstract

A description of the canonical formulation of lineal gravity minimally coupled to N point particles in a circular topology is given. The Hamiltonian is found to be equal to the time-rate of change of the extrinsic curvature multiplied by the proper circumference of the circle. Exact solutions for pure gravity and for gravity coupled to a single particle are obtained. The presence of a single particle significantly modifies the spacetime evolution by either slowing down or reversing the cosmological expansion of the circle, depending upon the choice of parameters.

51 pages, 24 eps figures, latex

References in corpus (5)

• Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles
• Exact Solutions to the Motion of Two Charged Particles in Lineal Gravity
• Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity
• Energy for N-Body Motion in Two Dimensional Gravity
• Exact Charged 2-Body Motion and the Static Balance Condition in Lineal Gravity

Cited by in corpus (6)

• Chaos in an Exact Relativistic 3-body Self-Gravitating System
• 3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System
• Dynamical N-body Equlibrium in Circular Dilaton Gravity
• Analysis of Two-Particle Systems in 2 + 1 Gravity Through Hamiltonian Dynamics
• One-Dimensional Relativistic Self-Gravitating Systems
• Dynamical Charged N-body Equilibrium in Circular Dilaton Gravity