Energy-momentum density in small regions: the classical pseudotensors

Details Energy-momentum density in small regions: the classical pseudotensors Energy-momentum density in small regions: the classical pseudotensors

2009-01-25

arxiv.org/abs/0901.3884v1

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.

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