Energy for N-body motion in two-dimensional gravity

Authors: Mann R.B.¹; Potvin G.¹; Raiteri M.²

Source: Classical and Quantum Gravity, Volume 17, Number 23, 2000 , pp. 4941-4958(18)

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Abstract:

A general definition of energy is given, via the N?ther theorem, for the N-body problem in [iopmath latex="$(1 + 1)$"] (1 + 1) [/iopmath] -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.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 2: Department of Mathematics, University of Torino, via C. Alberto 10, 10123 Torino, Italy

Publication date: 2000-01-01