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Precession of a gyroscope for the nonregular generalized finslerian metric gij = e2σ(x,y)aij(x)

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Abstract

The post-Newtonian problem of the precession of the axis of rotation of a gyroscope rotating around the earth in relation to distant stars belongs to a number of “nonclassical” verifications of the consequences of the theory of gravitation with an independent determination of the post-Newtonian parameters. A generalized Fermi-Walker transport equation is constructed and the problem of precession of a gyroscope is solved for the nonregular generalized Finslerian metric gij=e2σ(x,y)aij, where aij signifies the Riemannian metric tensor. The result contains a contribution in addition to the usual Riemannian PPN-terms, proportional to the parameter σa characterizing the dependence of σ on the speed of motion.

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Literature cited

  1. 1.

    H. Rund, Differential Geometry of Finsler Spaces, Springer, Berlin (1953).

  2. 2.

    G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories, D. Reidel, Dordrecht (1985).

  3. 3.

    M. Hashiguchi, Ana. Stiin ale Univ. “Al. I Cuza” din Iasi,30, 69–73 (1984).

  4. 4.

    R. Miron, J. Math. Kyoto Univ.,23, 219–224 (1983).

  5. 5.

    T. Okubo, Tensor O. S.,3, 48–55 (1940).

  6. 6.

    S. Watanabe, J. Nat. Acad. Math.,1, 79–85 (1983).

  7. 7.

    R. K. Tavakol and N. vanden Bergh, Phys. Lett.,112A, 23–25 (1985).

  8. 8.

    C. W. Misner, K. S. Torne, and J. A. Wheeler, Gravitation, Freeman, San Francisco (1973).

  9. 9.

    S. Watanabe and S. Ikeda, Tensor N. S.,40, 97–102 (1983).

  10. 10.

    S. Watanabe and S. Ikeda, Tensor N. S.,39, 37–41 (1982).

  11. 11.

    C. M. Will, Theory and Experiment in Gravitational Physics, Cambridge University Press, Cambridge (1981).

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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 91–95, May, 1989.

In conclusion, the author expresses deep gratitude to G. S. Asanov (MGU) for stating the problem and valuable comments.

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Aryngazin, A.K. Precession of a gyroscope for the nonregular generalized finslerian metric gij = e2σ(x,y)aij(x). Soviet Physics Journal 32, 398–401 (1989). https://doi.org/10.1007/BF00895325

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Keywords

  • Transport Equation
  • Independent Determination
  • Distant Star