Gravitational energy as Noether charge
Abstract
A definition of gravitational energy is proposed for any theory described by a diffeomorphisminvariant Lagrangian. The mathematical structure is a Noether current construction of Wald involving the boundary term in the action, but here it is argued that the physical interpretation of current conservation is conservation of energy. This leads to a quasilocal energy defined for compact spatial surfaces. The energy also depends on a vector generating a flow of time. Angular momentum may be similarly defined, depending on a choice of axial vector. For Einstein gravity: for the usual vector generating asymptotic time translations, the energy is the Bondi energy; for a stationary Killing vector, the energy is the Komar energy; in spherical symmetry, for the Kodama vector, the energy is the MisnerSharp energy. In general, the lack of a preferred time indicates the lack of a preferred energy, reminiscent of the energytime duality of quantum theory.
 Publication:

arXiv eprints
 Pub Date:
 April 2000
 arXiv:
 arXiv:grqc/0004042
 Bibcode:
 2000gr.qc.....4042H
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 4 pages, revtex