Everything about Stress-energy-momentum Pseudotensor totally explained
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 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.
Definition and properties of the Landau-Lifshitz pseudotensor
Landau &
Lifshitz were led by four requirements in their search for a gravitational energy momentum pseudotensor,
, which demonstrates the delocalisation of gravitational energy-momentum.
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