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arXiv · 2206.01322

The generalization of the ADM gravitational energy-momentum

J. B. Formiga·V. R. Gonçalves
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Abstract

In this paper, it is proved that the teleparallel energy-momentum generalizes that of the ADM formalism. In doing so, it is shown that the teleparallel $4$-momentum can be made to coincide with that of the ADM approach whenever the ADM $4$-momentum is applicable. The only assumptions are the time gauge for the teleparallel frame and the well-known restrictions for the coordinate system used in the calculation of the ADM $4$-momentum. Then, examples where the ADM formalism fails to give consist results, but the teleparallel approach does not, are given. The advantages of the teleparallel stress-energy tensor (density) over the pseudo-tensor of Landau-Lifshitz are exhibited. Finally, the difficulties in identifying the gravitational angular momentum density is discussed; it is shown that the spatial part of the proposed angular momentum density $M^{ab}$ vanishes when the teleparallel frame satisfies the time gauge condition.

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J. B. Formiga, V. R. Gonçalves. 2022-06-02. The generalization of the ADM gravitational energy-momentum. https://doi.org/10.1103/physrevd.106.044021

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