Stress–energy–momentum pseudotensor

In the theory of <a href="/facts/General_relativity/jVsoIg8X">general relativity</a>, a stress–energy–momentum pseudotensor, such as the Landau–Lifshitz pseudotensor, is an extension of the non-gravitational <a href="/facts/Stress%E2%80%93energy_tensor/wWKrzjfI">stress–energy tensor</a> that 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 <a href="/facts/Conserved_current/N4sFEG24">conserved current</a> within the framework of <a href="/facts/General_relativity/jVsoIg8X">general relativity</a>, so that the total energy–momentum crossing the <a href="/facts/Hypersurface/cTvtLVsV">hypersurface</a> (3-dimensional boundary) of any compact <a href="/facts/Space%E2%80%93time/uRIN1x4b">space–time</a> <a href="/facts/Hypervolume/vFQd0M7T">hypervolume</a> (4-dimensional submanifold) vanishes.
Some people (such as <a href="/facts/Erwin_Schr%C3%B6dinger/wCprepF2">Erwin Schrödinger</a>) have objected to this derivation on the grounds that <a href="/facts/Pseudotensor/CEW7VNgr">pseudotensors</a> are inappropriate objects in general relativity, but the conservation law only requires the use of the 4-<a href="/facts/Divergence/zpwwkFoU">divergence</a> of a pseudotensor which is, in this case, a tensor (which also vanishes). Mathematical developments in the 1980's have allowed pseudotensors to be understood as <a href="/facts/Section_(fiber_bundle)/DLnpXS5a">sections</a> of <a href="/facts/Jet_bundle/7RHyhv07">jet bundles</a>, thus providing a firm theoretical foundation for the concept of pseudotensors in general relativity.

Stress–energy–momentum pseudotensor open-in-new

Stress–energy–momentum pseudotensor