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Mappings of empty space-times leaving the curvature tensor invariant

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Abstract

It is shown that if in some local coordinate system the componentsR i jkl of the curvature tensor of an empty space-time are known, then, provided the space-time is not of Petrov typeN with hypersurface orthogonal geodesic rays, the components of the metric tensor are uniquely determined up to a trivial constant scaling factor. The Petrov type-N empty space-times with hypersurface orthogonal geodesic rays are investigated. The most general mappings leaving the curvature tensorR i jkl invariant are found for each class of these space-times.

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References

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

    Google Scholar 

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

    Google Scholar 

  3. McIntosh, C. B. G., and Haiford, W. D.J. Math. Phys. (to appear).

  4. Collinson, C. D. (1970).J. Math. Phys.,11, 818.

    Google Scholar 

  5. Brinkman, H. W. (1925).Math. Ann.,94, 119.

    Google Scholar 

  6. Newman, E., and Penrose, R. (1962).J. Math. Phys.,3, 565.

    Google Scholar 

  7. Collinson, C. D. (1969).J. Phys. A,2, 621.

    Google Scholar 

  8. Kundt, W. (1961).Z. Phys.,163, 77.

    Google Scholar 

  9. Robinson, I., and Trautman, A. (1962).Proc. R. Soc. London Ser. A,265, 463.

    Google Scholar 

  10. Hlavatý, V. (1959).J. Math. Mech.,8, 285.

    Google Scholar 

  11. Hlavatý, V. (1959).J. Math. Mech.,8, 597.

    Google Scholar 

  12. Hlavatý, V. (1960).J. Math. Mech.,9, 89.

    Google Scholar 

  13. Hlavatý, V. (1960).J. Math. Mech.,9, 453.

    Google Scholar 

  14. Hlavaty, V. (1961).J. Math. Mech.,10, 317.

    Google Scholar 

  15. Hlavatý, V. (1962).J. Math. Mech.,11, 35.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  18. Ihrig, E. (1976).Gen Rel. Grav.,7, 313.

    Google Scholar 

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

    Google Scholar 

  20. McIntosh, C. B. G., and Hall, G. preprint.

  21. Halford, W. D., McIntosh, C. G. G., and Van Leeuwen, E. H. (1980).J. Phys. A,13, 2995.

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Hull, Hull, England

    C. D. Collinson & Estelita da Graça Lopes Rodrigues Vaz

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  1. C. D. Collinson
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  2. Estelita da Graça Lopes Rodrigues Vaz
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Collinson, C.D., da Graça Lopes Rodrigues Vaz, E. Mappings of empty space-times leaving the curvature tensor invariant. Gen Relat Gravit 14, 5–15 (1982). https://doi.org/10.1007/BF00756191

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