Skip to main content
SpringerLink
Log in

Determination of the metric from the curvature

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

Abstract

A method of calculating the metric from the curvature is presented. Assuming that a tensor with the symmetry properties of a type D curvature tensor is given in an orthonormal tetrad, we use the Bianchi identities and the relationship between the connection and the tetrad in order to calculate, under certain assumptions, the corresponding metric. Some well-known metrics are derived from the curvature by using the method given here.

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. Schmidt, B. G. (1973).Commun. Math. Phys. 29, 55.

    Google Scholar 

  2. Edgar, S. B. (1991).J. Math. Phys. 32, 1011.

    Google Scholar 

  3. Cartan, E. (1946).Leçons sur la Géometrie des Espaces de Riemann (Gauthier-Villars, Paris).

    Google Scholar 

  4. Karlhede, A. (1980).Gen. Rel. Grav. 12, 693.

    Google Scholar 

  5. Ihrig, E. (1975).J. Math. Phys. 16, 54.

    Google Scholar 

  6. McIntosh, C. B. G., and Halford, W. D. (1981).J. Phys. A 14, 2331.

    Google Scholar 

  7. McIntosh, C. B. G., and Halford, W. D. (1982).J. Math. Phys. 23, 1149.

    Google Scholar 

  8. Hall, G. S., and McIntosh, C. B. G. (1983).Int. J. Theor. Phys. 22, 469.

    Google Scholar 

  9. Hall, G. S. (1983).Gen. Rel. Grav. 15, 581.

    Google Scholar 

  10. Hall, G. S. (1984).Gen. Rel. Grav. 16, 495.

    Google Scholar 

  11. Hall, G. S. (1984).Class. Quant. Grav. 1, 545.

    Google Scholar 

  12. Ihrig, E. (1975).Int. J. Theor. Phys. 14, 23.

    Google Scholar 

  13. Hall, G. S. (1984). InClassical General Relativity W. Bonner et al., eds. (Cambridge University Press, Cambridge).

    Google Scholar 

  14. Hall, G. S., and Kay, W. (1988).J. Math. Phys. 29, 420.

    Google Scholar 

  15. Synge, J. L. (1960).Relativity: The general theory (North-Holland, Amsterdam).

    Google Scholar 

  16. Pirani, F. A. E. (1956).Acta Phys. Polon. 15, 389.

    Google Scholar 

  17. Szekeres, P. (1965).J. Math. Phys. 6, 1387.

    Google Scholar 

  18. Ciufolini, I., and Demiański, M. (1986).Phys. Rev. D 34, 1018.

    Google Scholar 

  19. Hodgkinson, D. E. (1972).Gen. Rel. Grav. 3, 351.

    Google Scholar 

  20. Mashhoon, B. (1977).Astrophys. J. 216, 591.

    Google Scholar 

  21. Manoff, S. (1979).Gen. Rel. Grav. 11, 189.

    Google Scholar 

  22. Li, W., and Ni, W. (1979).J. Math. Phys. 20, 1473.

    Google Scholar 

  23. Bazański, S. L. (1989).J. Math. Phys. 30, 1794.

    Google Scholar 

  24. Quevedo, H. (1992).Gen. Rel. Grav. 24, 693.

    Google Scholar 

  25. Stephani, H. (1980)Allgemeine Relativitätstheorie (Deutscher Verlag der Wissenschaften, Berlin).

    Google Scholar 

  26. Quevedo, H. (1982). Diploma thesis, Patrice-Lumumba University, Moscow; (1984). “Erzeugung von Krümmungstensoren mittels einer Transformation ins Komplexe und Errechnen der entsprechenden Metriken”, University of Cologne report.

    Google Scholar 

  27. Demiański M. (1972).Phys. Lett. 42A, 157.

    Google Scholar 

  28. Demiański M. (1973).Acta Astr. Pol. 23, 197.

    Google Scholar 

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

    Google Scholar 

  30. Cahen, M., and Defrise, L. (1968).Commun. Math. Phys. 11, 56.

    Google Scholar 

  31. Hearn, A. C. (1987). REDUCEUser's Manual, version 3.3 (Rand Corporation CP78, Santa Monica, California).

    Google Scholar 

  32. Debever, R. (1964).Cahiers Phys. 18, 303.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Cologne, D-5000, Cologne 41, Federal Republic of Germany

    Hernando Quevedo

Authors
  1. Hernando Quevedo
    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

Quevedo, H. Determination of the metric from the curvature. Gen Relat Gravit 24, 799–819 (1992). https://doi.org/10.1007/BF00759087

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00759087

Keywords

Search

Navigation