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The Robertson-Walker metric and the symmetries belong to the family of contracted Ricci collineations

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Abstract

It is shown that the general form of the Robertson-Walker cosmological metric admits symmetry properties that are members of the symmetry family of contracted Ricci collineations. A particular form for the conservation law generator given by ▽ j [(−g)1/2(T j i −1/2δ jT i )ηi] = 0 following in consequence of these symmetries is obtained and interpreted.

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References

  1. Katzin, G. H., Levine, J., and Davis, W. R. (1969).J. Math. Phys.,10, 617; (1970).Tensor, N. S.,21, 52.

    Google Scholar 

  2. Singh, K. P., and Sharma, D. N. (1975).J. Phys. A: Math. Gen.,8, 1875.

    Google Scholar 

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

    Google Scholar 

  4. Katzin, G. H., Levine, J., and Davis, W. R. (1970).J. Math. Phys.,11, 1578.

    Google Scholar 

  5. Singh, K. P., and Sharma, D. N. (1973).Gen. Rel. Grav.,6, 397.

    Google Scholar 

  6. Katzin, G. H., and Levine, J. (1972).Colloquium Mathematicum (Poland) XXVI, 21.

    Google Scholar 

  7. Davis, W. R. (1974). “Conservation Laws in Einstein's General Theory of Relativity,” inLanczos Festschrift, ed. Scaife, B. K. P. (Academic Press, London), pp. 29–64.

    Google Scholar 

  8. Golab, S. (1972).Rep. Math. Phy. B, 3, 21.

    Google Scholar 

  9. Schouten, J. A. (1954).Rica-Calculus (Springer-Verlag, Berlin).

    Google Scholar 

  10. Collinson, C. D. (1970).Gen. Rel. Grav.,1, 137.

    Google Scholar 

  11. Trautman, A. (1962). “Conservation Laws in General Relativity,” inGravitation: An Introduction to Current Research, ed. Witten, L. John Wiley and Sons, New York, pp. 169–198.

    Google Scholar 

  12. Weinberg, S. (1972).Gravitation and Cosmology John Wiley and Sons, New York, pp. 412–415.

    Google Scholar 

  13. Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation (W. H. Freeman and Co., San Francisco), p. 558.

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, North Carolina State University, 27607, Raleigh, North Carolina

    L. H. Green, L. K. Norris, D. R. Oliver Jr. & W. R. Davis

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  1. L. H. Green
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  2. L. K. Norris
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  3. D. R. Oliver Jr.
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  4. W. R. Davis
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Green, L.H., Norris, L.K., Oliver, D.R. et al. The Robertson-Walker metric and the symmetries belong to the family of contracted Ricci collineations. Gen Relat Gravit 8, 731–736 (1977). https://doi.org/10.1007/BF00761783

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  • DOI: https://doi.org/10.1007/BF00761783

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