Covariant conservation laws from the palatini formalism |
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Authors: | Rainer Dick |
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Affiliation: | (1) Sektion Physik der Universität München, W-8000 Munich 2, Germany |
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Abstract: | Covariant conservation laws in the Palatini formalism are derived. The result indicates that the gravitational part of conserved charges in general relativity should be calculated from a combination of Komar's strongly conserved current and the Einstein tensor. This implies that the set of complete diffeomorphism charges of a gravitating system consisting of scalar matter is described by Komar's vector density, and that the identification of gravitational energy and momentum reduces to two choices: a choice of relative weights of the contributions resulting from Komar's current and from the Einstein tensor, and a choice of preferred vector fields in space-time. A proposal is made which yields energy and momentum as scalars under diffeomorphisms and as a Lorentz vector in tangent space. Furthermore, the result can be used to identify covariant conservation laws holding separately for the matter contributions to diffeomorphism charges. |
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