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The variational derivative of degenerate Lagrange densities

Published online by Cambridge University Press:  24 October 2008

Richard Pavelle
Richard Pavelle
Affiliation:
Department of Mathematics, The University of Arizona, Tucson, Arizona 85721
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Abstract

The variational derivative of Lagrange densities which are functions of the metric tensor and its first and second derivatives is considered. This tensor is generally of fourth order in the derivatives of the metric tensor. If derivatives of any order are not present in the variational derivative then the Lagrange density is said to be degenerate in these derivatives. An explicit expression for the variational derivative of Lagrange densities which are degenerate in third and/or fourth derivatives is displayed in tensor form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 167 - 172
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Eddington, A. S.The mathematical theory of relativity, Second Edition, section 61 (Cambridge University Press, Cambridge, 1954).Google Scholar
(2)Lovelock, D.The uniqueness of the Einstein Field equations in a four-dimensional space. Arch. Rational Mech. Anal. 33 (1969), 54–70.Google Scholar
(3)Lovelock, D.The Einstein tensor and its generalizations. J. Mathematical Phys. 12 (1971), 498–501. Eqs. (3.3) and (3.6).Google Scholar
(4)Buchdahl, H. A.On functionally constant invariants of the Riemann tensor. Proc. Cambridge Philos. Soc. 68 (1970), 179–185.Google Scholar
(5)Rund, H.Variational problems involving combined tensor fields. Abh. math. Sem. Univ. Hamburg 29 (1966), 243–262.Google Scholar