Energy for N-Body Motion in Two Dimensional Gravity
General Relativity and Quantum Cosmology
2009-10-31 v1
Abstract
A general definition of energy is given, via the N\"other theorem, for the N-body problem in (1+1) dimensional gravity. Within a first-order Lagrangian framework, the density of energy of a solution relative to a background is identified with the superpotential of the theory. For specific applications we reproduce the expected Hamiltonian for the motion of N particles in a curved spacetime. This Hamiltonian agrees with that found through an ADM-like prescription for the energy when the latter is applicable but it also extends to a wider class of solutions provided a suitable background is chosen.
Cite
@article{arxiv.gr-qc/0008072,
title = {Energy for N-Body Motion in Two Dimensional Gravity},
author = {R. B. Mann and G. Potvin and M. Raiteri},
journal= {arXiv preprint arXiv:gr-qc/0008072},
year = {2009}
}
Comments
Latex, 27 pages