Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-29T21:23:02.766Z Has data issue: false hasContentIssue false
  • English
  • Français

Applications of variational principles to classical perturbation theory in general relativity

Published online by Cambridge University Press:  24 October 2008

D. C. Robinson
D. C. Robinson
Affiliation:
Department of Mathematics, King's College, Strand, W.C. 2, London, England
Get access Rights & Permissions [Opens in a new window]

Abstract

The equations satisfied by perturbations of solutions of the Euler-Lagrange equations corresponding to a Lagrangian density L are derived from the first and second variations of L and these new Lagrangian densities are used to construct Noether and Euler identities. It is shown how these identities can be used in general relativity to construct conserved quantities and local uniqueness theorems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 2 , September 1975 , pp. 351 - 356
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Taub, A. H.Comm. Math. Phys. 15 (1969), 235.Google Scholar
(2)Morrey, C. B.Multiple integrals in the calculus of variations (Berlin, Springer, 1966).Google Scholar
(3)Goldberg, J. N. and Newman, E. T.J. Math. Phys. 10 (1969), 369.CrossRefGoogle Scholar
(4)Glass, E. N. and Goldberg, J. N.J. Math. Phys. 11 (1970), 3400.Google Scholar
(5)Carter, B.Phys. Rev. Lett. 26 (1971), 331.Google Scholar
(6)Carter, B. The general theory of stationary black hole states. In Black holes, ed. DeWitt, and DeWitt, (New York, Paris, London, Gordon and Breach, 1973).Google Scholar
(7)Trautman, A.Gravitation, ed. Witten, L., (New York, John Wiley and Sons, Inc., 1962).Google Scholar
(8)Robinson, D. C.Phys. Rev. D. 10 (1974), 458.CrossRefGoogle Scholar