Covariant decompositions of symmetric tensors in the theory of gravitation
Covariant orthogonal decompositions of symmetric tensors have proven to be of great interest in the theory of gravitation and in characterizing spaces of Riemannian metrics. The known transverse decomposition t and a transverse- traceless decomposition TT introduced recently are described and compared. The consistency and compatibility of these two procedures are demonstrated by showing that if Tsup(ab) is an arbitrary symmetric tensor, then Tsub(TT)sup(ab)=(Tsub(t)sup(ab))sub(TT)=(Tsub(TT)sup(ab))sub(t). The relationships of the various remaining longitudinal and trace parts of Tsup(ab) are exhibited. It is found that every transverse tensor can be uniquely and orthogonally decomposed into a sum of a transverse-traceless part and another part that is transverse but has in general a non vanishing trace. Physical interpretation of the reaction between transverse and transverse-traceless tensors is provided by the canonical momentum of a gravitational field. Geometrical interpretation follows from considering the structure of the space of conformal metrics on closed manifolds. (FR)
- Research Organization:
- North Carolina Univ., Chapel Hill (USA)
- NSA Number:
- NSA-33-013887
- OSTI ID:
- 4100327
- Journal Information:
- Ann. Inst. Henri Poincare, Sect. A, v. 21, no. 4, pp. 319-332, Journal Name: Ann. Inst. Henri Poincare, Sect. A, v. 21, no. 4, pp. 319-332; ISSN AHPAA
- Country of Publication:
- France
- Language:
- English
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