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On the problem of uniqueness of energy-momentum tensor of gravitational field

A. I. Nikishov
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Abstract

For an island-like distribution of matter the gravitational energy-momentum tensor is defined according to Weinberg as a source of metric. If this source is formed by self-interactions of gravitons, so that nonphysical degrees of freedom are excluded, then this source is a reasonable candidate for the energy-momentum tensor of gravitational field. The disastrous influence of the nonphysical degrees of freedom is demonstrated by comparing the gravitational energy-momentum tensors in the harmonic, isotropic and standard frames for the Schwarzschild solution. The harmonic frame is clearly preferable for defining the gravitational energy-momentum tensor.

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A. I. Nikishov. 2003-10-14. On the problem of uniqueness of energy-momentum tensor of gravitational field. https://arxiv.org/abs/gr-qc/0310072

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