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Energy for N-Body Motion in Two Dimensional Gravity

R. B. Mann·G. Potvin·M. Raiteri
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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.

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R. B. Mann, G. Potvin, M. Raiteri. 2000-08-29. Energy for N-Body Motion in Two Dimensional Gravity. https://doi.org/10.1088/0264-9381%2F17%2F23%2F311

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