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A Symplectic Hamiltonian Derivation of Quasilocal Energy-Momentum for GR | Chiang-Mei Chen
; James M. Nester
; | Date: |
27 Dec 1999 | Journal: | Grav.Cosmol. 6 (2000) 257-270 | Subject: | gr-qc | Abstract: | The various roles of boundary terms in the gravitational Lagrangian and Hamiltonian are explored. A symplectic Hamiltonian-boundary-term approach is ideally suited for a large class of quasilocal energy-momentum expressions for general relativity. This approach provides a physical interpretation for many of the well-known gravitational energy-momentum expressions including all of the pseudotensors, associating each with unique boundary conditions. From this perspective we find that the pseudotensors of Einstein and M{o}ller (which is closely related to Komar’s superpotential) are especially natural, but the latter has certain shortcomings. Among the infinite possibilities, we found that there are really only two Hamiltonian-boundary-term quasilocal expressions which correspond to {em covariant} boundary conditions; they are respectively of the Dirichlet or Neumann type. Our Dirichlet expression coincides with the expression recently obtained by Katz and coworkers using Noether arguments and a fixed background. A modification of their argument yields our Neumann expression. | Source: | arXiv, gr-qc/0001088 | Services: | Forum | Review | PDF | Favorites |
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