Pseudotensor

In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation preserving coordinate transformation (e.g., a proper rotation), but additionally changes sign under an orientation reversing coordinate transformation (e.g., an improper rotation, which is a transformation that can be expressed as a proper rotation followed by reflection).

There is a second meaning for pseudotensor, restricted to general relativity; tensors obey strict transformation laws, whilst pseudotensors are not so constrained. Consequently the form of a pseudotensor will, in general, change as the frame of reference is altered. An equation which holds in a frame containing pseudotensors will not necessarily hold in a different frame; this makes pseudotensors of limited relevance because equations in which they appear are not invariant in form.

Read more about PseudotensorDefinition, Examples

Other articles related to "pseudotensor, pseudotensors":

Stress–energy–momentum Pseudotensor - Einstein Pseudotensor
... This pseudotensor was originally developed by Albert Einstein ... Paul Dirac showed that the mixed Einstein pseudotensor satisfies a conservation law Clearly this pseudotensor for gravitational stress–energy is constructed ... of the metric vanish because each term in the pseudotensor is quadratic in the first derivatives of the metric ...
Stress–energy–momentum Pseudotensor - Landau–Lifshitz Pseudotensor
... 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 ... matter stress–energy–momentum tensor from the combined pseudotensor results in the gravitational stress–energy–momentum pseudotensor ...
Gravitational Energy - General Relativity
... It is sometimes modeled via the Landau-Lifshitz pseudotensor which allows the energy-momentum conservation laws of classical mechanics to be retained ... Addition of the matter stress-energy-momentum tensor to the Landau-Lifshitz pseudotensor results in a combined matter plus gravitational energy pseudotensor which has a vanishing 4-divergenc ... Some people object to this derivation on the grounds that pseudotensors are inappropriate in general relativity, but the divergence of the combined matter plus gravitational energy pseudotensor is ...
Stress–energy–momentum Pseudotensor - Landau–Lifshitz Pseudotensor - Verification
... The Landau–Lifshitz pseudotensor is constructed so that when added to the stress–energy tensor of matter, its total 4-divergence vanishes ... The Landau–Lifshitz pseudotensor appears to include second derivative terms in the metric, but in fact the explicit second derivative terms in the ... This is more evident when the pseudotensor is directly expressed in terms of the metric tensor or the Levi-Civita connection only the first derivative terms in the metric survive and ...
Pseudotensor - Examples
... as such, an integrand is an example of a pseudotensor density according to the first definition ...