Abstract
The operational and canonical definitions of an energy-momentum tensor (EMT) are considered as well as the tensor and nontensor conservation laws. It is shown that the canonical EMT contradicts the experiments and the operational definition, the Belinfante-Rosenfeld procedure worsens the situation, and the nontensor “conservation laws” are meaningless. A definition of the 4-momentum of a system demands a translator since integration of vectors is meaningless. The mass of a fluid sphere is calculated. It is shown that, according to the standard energy-momentum pseudotensor, the mass-energy of a gravitational field is positive. This contradicts the idea of a negative gravitational energy and discredits the pseudotensor. And what is more, integral 4-pseudovectors are meaningless in general since reference frames for their components are not determined even for coordinates which are Minkowskian at infinity.
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Khrapko, R.I. The truth about the energy-momentum tensor and pseudotensor. Gravit. Cosmol. 20, 264–273 (2014). https://doi.org/10.1134/S0202289314040082
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DOI: https://doi.org/10.1134/S0202289314040082