Energy for N-Body Motion in Two Dimensional Gravity

Abstract

A general definition of energy is given, via the Nöther 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.

Latex, 27 pages

References in corpus (4)

• Relativistic conservation laws and integral constraints for large cosmological perturbations
• The Entropy of Taub-Bolt Solution
• Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity
• (2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame

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• N-body Gravity and the Schroedinger Equation
• Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems
• Particles on a Circle in Canonical Lineal Gravity
• The relative energy of homogeneous and isotropic universes from variational principles
• One-Dimensional Relativistic Self-Gravitating Systems
• Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis)