Skip to main content
SpringerLink
Log in

On axially symmetric solutions of Einstein's field equations in matter and an example of static gravitational shielding

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

Abstract

A model system, consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM. The stresses in the shell are not of the canonical Weyl type, and it is argued that the same is true for more realistic situations, e.g., rotating matter. Owing to the nonlinearity of Einstein's field equations, the field of the point mass is shielded from the interior of the shell by a factor η lying between 1–3M/R and 1–2M/R, and the field outside the shell explicitly depends onR.

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. Geroch, R. (1971).J. Math. Phys.,12, 918; (1972).J. Math. Phys.,13, 394.

    Google Scholar 

  2. Cosgrove, Ch. M. (1980).J. Math. Phys.,21, 2417.

    Google Scholar 

  3. Kramer, D., Stephani, H., MacCallum, M., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (VEB Deutscher Verlag der Wissenschaften, Berlin).

    Google Scholar 

  4. Weyl, H. (1917).Ann. Phys. (Leipzig),54, 117.

    Google Scholar 

  5. Weyl, H. (1919).Ann. Phys. (Leipzig),59, 185.

    Google Scholar 

  6. Bach, R., and Weyl, H. (1922).Math. Z.,13, 134.

    Google Scholar 

  7. Forward, R. L. (1982).Phys. Rev. D,26, 735.

    Google Scholar 

  8. Weber, J. (1966).Phys. Rev.,146, 935.

    Google Scholar 

  9. Dietz, W., and Hoenselaers, C. (1982).Phys. Rev. Lett.,48, 778.

    Google Scholar 

  10. Trümper, M. (1967).Z. Naturforschung,22a, 1347.

    Google Scholar 

  11. Brill, D. R., and Cohen J. M. (1966).Phys. Rev.,143, 1011.

    Google Scholar 

  12. Whittaker, E. T., and Watson, G. N. (1927).A Course of Modern Analysis (Cambridge University Press, Cambridge), p. 332.

    Google Scholar 

  13. Cohen, J. M. (1967).J. Math. Phys.,8, 1477.

    Google Scholar 

  14. Levy, H. (1968).Nuovo Cimento,56B, 253.

    Google Scholar 

  15. Marek, J., and Sloane, A. (1979).Nuovo Cimento,51B, 45.

    Google Scholar 

  16. Haggag, S., and Marek, J. (1981).Nuovo Cimento,62B, 273.

    Google Scholar 

  17. Israel, W. (1977).Phys. Rev. D,15, 935.

    Google Scholar 

  18. Weinberg, S. (1972).Gravitation and Cosmology (John Wiluey, New York).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik der Universität Tübingen, Tübingen, Federal Republic of Germany

    H. Pfister

  2. Max-Planck-Institut für Astrophysik, Garching b. München, Federal Republic of Germany

    H. Pfister

  3. Institut für Theoretische Physik der Universität Tübingen, Tübingen, Federal Republic of Germany

    W. Konrad

Authors
  1. H. Pfister
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Konrad
    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

Pfister, H., Konrad, W. On axially symmetric solutions of Einstein's field equations in matter and an example of static gravitational shielding. Gen Relat Gravit 16, 979–1001 (1984). https://doi.org/10.1007/BF00760102

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00760102

Keywords

Search

Navigation