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.

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