Skip to main content
SpringerLink
Log in

Algebraic determination of the metric from the curvature in general relativity

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The general solution for a symmetric second-order tensorX of the equationX e(a R e b cd=0 whereR is the Riemann tensor of a space-time manifold, andX is obtained in terms of the curvature 2-form structure ofR by a straightforward geometrical technique, and agrees with that given by McIntosh and Halford using a different procedure. Two results of earlier authors are derived as simple corollaries of the general theorem.

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

  • Churchill, R. V. (1932).Transactions of the American Mathematical Society,34, 784.

    MathSciNet  Google Scholar 

  • Collinson, C. D. (1970).Journal of Mathematical Physics,11, 818.

    Article  Google Scholar 

  • Collinson, C. D., and da Graça Lopes Rodrigues Vaz (1981). “Mappings of Empty Space-Times Leaving the Curvature Tensor Invariant,” preprint, University of Hull, England.

    Google Scholar 

  • Hall, G. S. (1976).Journal of Physics A,9, 541.

    Google Scholar 

  • Hall, G. S. (1979). “The Classification of Second Order Symmetric Tensors in General Relativity Theory,” Lectures given at the Stefan Banach International Mathematical Centre, Warsaw, (preprint—to appear).

  • Hall, G. S. (1982). “Curvature Collineations and the Determination of the Metric from the curvature in General Relativity,” preprint, University of Aberdeen, Scotland, U.K.

    Google Scholar 

  • Ihrig, E. (1975a).Journal of Mathematical Physics,16, 54.

    Article  Google Scholar 

  • Ihrig, E. (1975b).International Journal of Theoretical Physics,14, 23.

    Article  Google Scholar 

  • Ihrig, E. (1976).General Relativity and Gravitation,7, 313.

    Article  Google Scholar 

  • Katzin, G. H., Levine, J., and Davis, W. R. (1969).Journal of Mathematical Physics,10, 617.

    Article  Google Scholar 

  • McIntosh, C. B. G., and Halford, W. D. (1982).Journal of Mathematical Physics, (to appear).

  • McIntosh, C. B. G., and Halford, W. D. (1981b). “Determination of the Metric Tensor from Components of the Riemann Tensor,”Journal of Physics A,14, 2331.

    Google Scholar 

  • McIntosh, C. B. G., and Van Leeuwen, E. H. (1982).Journal of Mathematical Physics, (to appear).

  • Plebański, J. (1964).Acta Physica Polonica,26, 963.

    Google Scholar 

  • Pirani, F. A. E. (1956).Acta Physica Polonica,15, 389.

    Google Scholar 

  • Szekeres, P. (1965).Journal of Mathematical Physics,6, 1387.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Aberdeen, The Edward Wright Building, Dunbar Street, AB9 2TY, Aberdeen, Scotland

    G. S. Hall

  2. Department of Mathematics, Monash University, 3168, Clayton, Victoria, Australia

    C. B. G. McIntosh

Authors
  1. G. S. Hall
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. B. G. McIntosh
    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

Hall, G.S., McIntosh, C.B.G. Algebraic determination of the metric from the curvature in general relativity. Int J Theor Phys 22, 469–476 (1983). https://doi.org/10.1007/BF02083290

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02083290

Keywords

Search

Navigation