Algebraic determination of the metric from the curvature in general relativity

  • G. S. Hall
  • C. B. G. McIntosh


The general solution for a symmetric second-order tensorX of the equationXe(aR 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.


Manifold Field Theory General Relativity Elementary Particle Quantum Field Theory 
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  1. Churchill, R. V. (1932).Transactions of the American Mathematical Society,34, 784.MathSciNetGoogle Scholar
  2. Collinson, C. D. (1970).Journal of Mathematical Physics,11, 818.CrossRefGoogle Scholar
  3. 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
  4. Hall, G. S. (1976).Journal of Physics A,9, 541.Google Scholar
  5. 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).Google Scholar
  6. 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
  7. Ihrig, E. (1975a).Journal of Mathematical Physics,16, 54.CrossRefGoogle Scholar
  8. Ihrig, E. (1975b).International Journal of Theoretical Physics,14, 23.CrossRefGoogle Scholar
  9. Ihrig, E. (1976).General Relativity and Gravitation,7, 313.CrossRefGoogle Scholar
  10. Katzin, G. H., Levine, J., and Davis, W. R. (1969).Journal of Mathematical Physics,10, 617.CrossRefGoogle Scholar
  11. McIntosh, C. B. G., and Halford, W. D. (1982).Journal of Mathematical Physics, (to appear).Google Scholar
  12. 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
  13. McIntosh, C. B. G., and Van Leeuwen, E. H. (1982).Journal of Mathematical Physics, (to appear).Google Scholar
  14. Plebański, J. (1964).Acta Physica Polonica,26, 963.Google Scholar
  15. Pirani, F. A. E. (1956).Acta Physica Polonica,15, 389.Google Scholar
  16. Szekeres, P. (1965).Journal of Mathematical Physics,6, 1387.CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • G. S. Hall
    • 1
  • C. B. G. McIntosh
    • 2
  1. 1.Department of MathematicsUniversity of Aberdeen, The Edward Wright BuildingAberdeenScotland
  2. 2.Department of MathematicsMonash UniversityClaytonAustralia

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