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On the parameterization dependence of the energy momentum tensor and the metric

N. E. J. Bjerrum-Bohr·John F. Donoghue·Barry R. Holstein
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Abstract

We use results by Kirilin to show that in general relativity the nonleading terms in the energy-momentum tensor of a particle depends on the parameterization of the gravitational field. While the classical metric that is calculated from this source, used to define the leading long-distance corrections to the metric, also has a parameteriztion dependence, it can be removed by a coordinate change. Thus the classical observables are parameterization independent. The quantum effects that emerge within the same calculation of the metric also depend on the parameterization and a full quantum calculation requires the inclusion of further diagrams. However, within a given parameterization the quantum effects calculated by us in a previous paper are well defined. Flaws of Kirilin's proposed alternate metric definition are described and we explain why the diagrams that we calculated are the appropriate ones.

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N. E. J. Bjerrum-Bohr, John F. Donoghue, Barry R. Holstein. 2006-10-19. On the parameterization dependence of the energy momentum tensor and the metric. https://doi.org/10.1103/physrevd.75.108502

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