Stress-energy-momentum pseudotensor

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In the theory of general relativity, the stress-energy-momentum pseudotensor or Landau-Lifshitz pseudotensor allows the energy-momentum of a system of gravitating matter to be defined; in particular it allows the total matter plus the gravitating energy-momentum to form a conserved current within the framework of general relativity, so that the total energy-momentum crossing the hypersurface of any closed space-time hypervolume vanishes.

The use of the Landau-Lifshitz combined matter+gravitational stress-energy-momentum pseudotensor^[1] allows the energy-momentum conservation laws to be extended into general relativity. Subtraction of the matter stress-energy-momentum tensor from the combined pseudotensor results in the gravitational stress-energy-momentum pseudotensor. Some people object to this derivation on the grounds that pseudotensors are inappropriate objects in general relativity, but this treatment only requires the use of the 4-divergence of a pseudotensor which is, in this case, a tensor. On the other hand, most pseudotensors are sections of jet bundles, which are perfectly valid objects in GR.