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arXiv · 0901.3884

Energy-momentum density in small regions: the classical pseudotensors

Lau Loi So·James M. Nester·Hsin Chen
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Abstract

The values for the gravitational energy-momentum density, given by the famous classical pseudotensors: Einstein, Papapetrou, Landau-Lifshitz, Bergmann-Thompson, Goldberg, Møller, and Weinberg, in the small region limit are found to lowest non-vanishing order in normal coordinates. All except Møller'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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Lau Loi So, James M. Nester, Hsin Chen. 2009-01-25. Energy-momentum density in small regions: the classical pseudotensors. https://doi.org/10.1088/0264-9381%2F26%2F8%2F085004

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