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

TL;DR

This paper investigates how the parameterization of the gravitational field affects the energy-momentum tensor and metric in general relativity, distinguishing between classical and quantum effects and emphasizing the importance of coordinate choices.

Contribution

It clarifies the parameterization dependence of classical and quantum metrics and defends the authors' diagrammatic approach against alternative definitions.

Findings

Classical metric parameterization dependence can be removed by coordinate change.

Quantum effects depend on parameterization and require additional diagrams for full calculation.

The authors' previous quantum calculations are well-defined within a fixed parameterization.

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.