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A Class of Conserved Tensors in an Arbitrary Gravitational Field

Published online by Cambridge University Press:  24 October 2008

C. D. Collinson
C. D. Collinson
Affiliation:
Department of Mathematics King's CollegeLondon
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Abstract

Four-index tensors with all possible terms either (a) quadratic in the Riemann curvature tensor, or (b) linear in its second derivatives, with coefficients constructed from products of metric tensors, are enumerated for the case of Riemannian space-time. All linear combinations of these which have zero divergence, and which might therefore be associated with the super-energy in gravitational theory, are found by elementary methods. The only independent such combination reduces in empty space-time to the tensor previously found by Bel and Robinson.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 346 - 362
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

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