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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). In this sense, it is a generalization of a pseudovector. There is a second meaning for pseudotensor, restricted to general relativity; tensors obey strict transformation laws, but pseudotensors are not so constrained. Consequently, the form of a pseudotensor will, in general, change as the frame of reference is altered. An equation containing pseudotensors which holds in a one frame 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. ==Definition== Two quite different mathematical objects are called a pseudotensor in different contexts. The first context is essentially a tensor multiplied by an extra sign factor, such that the pseudotensor changes sign under reflections when a normal tensor does not. According to one definition, a pseudotensor P of the type is a geometric object whose components in an arbitrary basis are enumerated by indices and obey the transformation rule : under a change of basis.〔Sharipov, R.A. (1996). Course of Differential Geometry, Ufa:Bashkir State University, Russia, p. 34, eq. 6.15. ISBN 5-7477-0129-0, 〕〔Lawden, Derek F. (1982). An Introduction to Tensor Calculus, Relativity and Cosmology. Chichester:John Wiley & Sons Ltd., p. 29, eq. 13.1. ISBN 0-471-10082-X〕〔Borisenko, A. I. and Tarapov, I. E. (1968). Vector and Tensor Analysis with Applications, New York:Dover Publications, Inc., p. 124, eq. 3.34. ISBN 0-486-63833-2〕 Here are the components of the pseudotensor in the new and old bases, respectively, . This transformation rule differs from the rule for an ordinary tensor in the intermediate treatment only by the presence of the factor (−1)''A''. The second context where the word "pseudotensor" is used is general relativity. In that theory, one cannot describe the energy and momentum of the gravitational field by an energy–momentum tensor. Instead, one introduces objects that behave as tensors only with respect to restricted coordinate transformations. Strictly speaking, such objects are not tensors at all. A famous example of such a pseudotensor is the Landau–Lifshitz pseudotensor. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「pseudotensor」の詳細全文を読む スポンサード リンク
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