Particles on a Circle in Canonical Lineal Gravity
General Relativity and Quantum Cosmology
2009-11-07 v1
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.
Cite
@article{arxiv.gr-qc/0105008,
title = {Particles on a Circle in Canonical Lineal Gravity},
author = {R. B. Mann},
journal= {arXiv preprint arXiv:gr-qc/0105008},
year = {2009}
}
Comments
51 pages, 24 eps figures, latex