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Stress–energy–momentum pseudotensor
In the theory of general relativity, a stress–energy–momentum pseudotensor, such as the Landau–Lifshitz pseudotensor, is an extension of the non-gravitational stress–energy tensor which incorporates the energy–momentum of gravity. It allows the energy–momentum of a system of gravitating matter to be defined. In particular it allows the total of 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 (3-dimensional boundary) of ''any'' compact space–time hypervolume (4-dimensional submanifold) vanishes.
Some people (such as Erwin Schrödinger) have objected to this derivation on the grounds that pseudotensors are inappropriate objects in general relativity, but the conservation law only requires the use of the 4-divergence of a pseudotensor which is, in this case, a tensor (which also vanishes). Also, most pseudotensors are sections of jet bundles, which are now recognized as perfectly valid objects in GR.
==Landau–Lifshitz pseudotensor==
The use of the Landau–Lifshitz combined matter+gravitational stress–energy–momentum pseudotensor〔Lev Davidovich Landau & Evgeny Mikhailovich Lifshitz, ''The Classical Theory of Fields'', (1951), Pergamon Press, ISBN 7-5062-4256-7 chapter 11, section #96〕 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.
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