Energy for N-Body Motion in Two Dimensional Gravity

Details Energy for N-Body Motion in Two Dimensional Gravity Energy for N-Body Motion in Two Dimensional Gravity

2000-08-29

arxiv.org/abs/gr-qc/0008072v1

Class.Quant.Grav. 17 (2000) 4941-4958

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 27 pages

Scientific paper

10.1088/0264-9381/17/23/311

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.

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