Stress–energy–momentum pseudotensor: Difference between revisions

Undid revision 361421339 by BenRG (talk)
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(Undid revision 361421339 by BenRG (talk))
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 object to this derivation on the grounds that [[pseudotensor]]s 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 bundle]]s, which are perfectly valid objects in GR.
 
==Landau–Lifshitz pseudotensor==