Skip to main content
SpringerLink
Log in

Lagrangian methods and nonlinear high-frequency gravitational waves

  • Research Articles
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

An iterative procedure using Whitham's averaged Lagrangian technique and a two-parameter expansion of the metric tensor to investigate nonlinear high-frequency gravitational waves is developed. It is shown that, as a result of the nonlinearity, high-frequency gravitational waves are no longer restricted to propagate along null geodesics as in the linear theory. It is also shown that, to the order of approximation investigated, the theory is gauge invariant.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Araujo, M. E. (1986).Gen. Rel. Grav.,18, 219.

    Google Scholar 

  2. Whitham, G. B. (1974).Linear and Nonlinear Waves (Wiley-Interscience, New York), Chaps. 11 and 14.

    Google Scholar 

  3. MacCallum, M. A. H., and Taub, A. H. (1973).Commun. Math. Phys.,30, 153.

    Google Scholar 

  4. Landau, L. D., and Lifshitz, E. M. (1975).The Classical Theory of Fields, 4th English ed. (Pergamon, Oxford), Sect. 94.

    Google Scholar 

  5. Dougherty, J. P. (1970).J. Plasma Phys.,4, 761.

    Google Scholar 

  6. Isaacson, R. A. (1968).Phys. Rev.,166, 1263.

    Google Scholar 

  7. Isaacson, R. A. (1968).Phys. Rev.,166, 1272.

    Google Scholar 

  8. Brill, D., and Hartle, J. B. (1964).Phys. Rev. B,135, 271.

    Google Scholar 

Download references

Author information

Author notes

  1. M. E. Araujo

    Present address: Departamento de Matemática, Universidade de Brasília (UnB), 70.910, Brasília, D.F., Brazil

Authors and Affiliations

  1. School of Mathematical Sciences, Queen Mary College, Mile end Road, E1 4NS, London, UK

    M. E. Araujo

Authors
  1. M. E. Araujo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Araujo, M.E. Lagrangian methods and nonlinear high-frequency gravitational waves. Gen Relat Gravit 21, 323–348 (1989). https://doi.org/10.1007/BF00760437

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00760437

Keywords

Search

Navigation