Skip to main content
SpringerLink
Log in

Einstein's equations near spatial infinity

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

A new class of space-times is introduced which, in a neighbourhood of spatial infinity, allows an expansion in negative powers of a radial coordinate. Einstein's vacuum equations give rise to a hierarchy of linear equations for the coefficients in this expansion. It is demonstrated that this hierarchy can be completely solved provided the initial data satisfy certain constraints.

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. Bondi, H., van der Burg, M. G. J., Metzner, A. W. K.: Proc. R. Soc.A269, 21–52 (1962)

    Google Scholar 

  2. Penrose, R.: Proc. R. Soc.A284, 159–203 (1965)

    Google Scholar 

  3. Friedrich, H.: Proc. R. Soc.A378, 401–421 (1981)

    Google Scholar 

  4. Ashtekar, A., Hansen, R. O.: J. Math. Phys.19, 1542–1566 (1978)

    Google Scholar 

  5. Schmidt, B. G., Stewart, J. M.: Proc. R. Soc.A367, 503–525 (1979); Porrill, J., Stewart, J. M.: Proc. R. Soc.A376, 451–463 (1981); Bardeen, J. M., Press, W. H.: J. Math. Phys.14, 7–19 (1973)

    Google Scholar 

  6. Geroch, R.: In: Asymptotic structure of space-time, Esposito, F. P., Witten, L. (eds.) pp. 1–105, New York: Plenum 1977

    Google Scholar 

  7. Sommers, P.: Math. Phys.19, 549–554 (1978)

    Google Scholar 

  8. Beig, R., Simon, W.: Commun. Math. Phys.78, 75–82 (1980)

    Google Scholar 

  9. Beig, R., Simon, W.: Proc. R. Soc.A376, 333–341 (1981)

    Google Scholar 

  10. Dray, T.: G.R.G.14, 109 (1982)

    Google Scholar 

  11. Schmidt, B. G.: Commun. Math. Phys.78, 447–454 (1981)

    Google Scholar 

  12. Eardley, D.: Thesis, Univ. of Berkeley 1971

  13. Ashtekar, A.: In: General relativity and gravitation, Vol. 2, Held, A. (ed.) pp. 37–69. New York: Plenum 1980

    Google Scholar 

  14. Bergmann, P.: Phys. Rev.124, 274–278 (1961)

    Google Scholar 

  15. Schouten, J. A.: Ricci-Calculus. Berlin: Springer 1954

    Google Scholar 

  16. Fischer, A. E., Marsden, J. E.: J. Math. Phys.13, 546–568 (1972)

    Google Scholar 

  17. Arnowitt, R., Deser, S., Misner, C. W.: In: Gravitation, Witten L. (ed.) pp. 227–265, New York: Wiley 1962

    Google Scholar 

  18. Beig, R.: (to be published)

  19. Choquet-Bruhat, Y.: In: Gravitation, Witten, L. (ed.). pp. 130–168. New York: Wiley 1962

    Google Scholar 

  20. Christodoulou, D., o'Murchadha, N.: Commun. Math. Phys.80, 271–300 (1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Wien, Wien, Austria

    R. Beig

  2. Max-Planck-Institut für Physik und Astrophysik, Institu für Astrophysik, D-8000, München, Germany

    B. G. Schmidt

Authors
  1. R. Beig
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. G. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by S.-T. Yau

Work supported by “Fonds zur Förderung der wissenschaftlichen Forschung in Österreich,” Project no. 4069

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beig, R., Schmidt, B.G. Einstein's equations near spatial infinity. Commun.Math. Phys. 87, 65–80 (1982). https://doi.org/10.1007/BF01211056

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01211056

Keywords

Search

Navigation