Stress–energy–momentum pseudotensor: Difference between revisions

Undid revision 796718488 by Ciphers (talk) A pseudotensor cannot be called a tensor and "e.g." does not go before "such as"
(Undid revision 796718488 by Ciphers (talk) A pseudotensor cannot be called a tensor and "e.g." does not go before "such as")
In the theory of [[general relativity]], a '''stress–energy–momentum pseudotensor''' (e.g., 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.
 
This tensor allows the definition of [[energy–momentum]] system of the gravitating matter. 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) ends up vanishing.
 
Some people (such as [[Erwin Schrödinger]]{{citation needed|date=October 2015}}) have objected 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 now recognized as perfectly valid objects in GR.