NDLI: Gauge-invariant localization of infinitely many gravitational energies from all possible auxiliary structures

Content Provider	Springer Nature Link
Author	Pitts, J. Brian
Copyright Year	2009
Abstract	The problem of finding a covariant expression for the distribution and conservation of gravitational energy–momentum dates to the 1910s. A suitably covariant infinite-component localization is displayed, reflecting Bergmann’s realization that there are infinitely many conserved gravitational energy–momenta. Initially use is made of a flat background metric (or rather, all of them) or connection, because the desired gauge invariance properties are obvious. Partial gauge-fixing then yields an appropriate covariant quantity without any background metric or connection; one version is the collection of pseudotensors of a given type, such as the Einstein pseudotensor, in every coordinate system. This solution to the gauge covariance problem is easily adapted to any pseudotensorial expression (Landau–Lifshitz, Goldberg, Papapetrou or the like) or to any tensorial expression built with a background metric or connection. Thus the specific functional form can be chosen on technical grounds such as relating to Noether’s theorem and yielding expected values of conserved quantities in certain contexts and then rendered covariant using the procedure described here. The application to angular momentum localization is straightforward. Traditional objections to pseudotensors are based largely on the false assumption that there is only one gravitational energy rather than infinitely many.
Starting Page	601
Ending Page	622
Page Count	22
File Format	PDF
ISSN	00017701
Journal	General Relativity and Gravitation
Volume Number	42
Issue Number	3
e-ISSN	15729532
Language	English
Publisher	Springer US
Publisher Date	2009-08-12
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Conservation laws Localization Gauge invariance Infinite-component Gravitational energy Astronomy, Astrophysics and Cosmology Differential Geometry Classical and Quantum Gravitation, Relativity Theory Theoretical, Mathematical and Computational Physics Quantum Physics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

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