Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-01-25
Class.Quant.Grav.26:085004,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
13 pages
Scientific paper
10.1088/0264-9381/26/8/085004
The values for the gravitational energy-momentum density, given by the famous classical pseudotensors: Einstein, Papapetrou, Landau-Lifshitz, Bergmann-Thompson, Goldberg, M{\o}ller, and Weinberg, in the small region limit are found to lowest non-vanishing order in normal coordinates. All except M{\o}ller's have the zeroth order material limit required by the equivalence principle. However for small vacuum regions we find that {\it none} of these classical holonomic pseudotensors satisfies the criterion of being proportional to the Bel-Robinson tensor. Generalizing an earlier work which had identified one case, we found another independent linear combination satisfying this requirement--and hence a one parameter set of linear combinations of the classical pseudotensors with this desirable property.
Chen Hsin
Nester James M.
So Lau Loi
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