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The Energy-Momentum Tensor for the Gravitational Field

S. V. Babak·L. P. Grishchuk
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Abstract

The field theoretical description of the general relativity (GR) is further developed. The action for the gravitational field and its sources is given explicitely. The equations of motion and the energy-momentum tensor for the gravitational field are derived by applying the variational principle. We have succeeded in constructing the unique gravitational energy-momentum tensor which is 1) symmetric, 2) conserved due to the field equations, and 3) contains not higher than the first order derivatives of the field variables. It is shown that the Landau-Lifshitz pseudotensor is an object most closely related to the derived energy-momentum tensor.

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S. V. Babak, L. P. Grishchuk. 1999-04-01. The Energy-Momentum Tensor for the Gravitational Field. https://arxiv.org/abs/gr-qc/9904002

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