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Proposal for the proper gravitational energy-momentum tensor

We propose a gravitational energy-momentum tensor of the general relativity obtained using Noethers theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the gravitational energy-momentum tensor labels a local Lorentz frame that satisfies the energy-momentum conservation law. The energies for a gravitational wave and a Friedmann-Lemaitre--Robertson--Walker universe are calculated as examples.

preprint2017arXivOpen access
Katsutaro Shimizu
gr-qc
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Katsutaro Shimizu

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