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On the exterior gravitational field of a mass with a multipole moment

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Abstract

Recently, Gutsunaev and Manko [6] presented a procedure for obtaining new static axisymmetric solutions of Einstein's vacuum field equations from a known one. We show that this procedure is based on the property that the derivatives of a harmonic function are harmonic. The special case of a metric with mass and quadrupole moment is investigated and compared with the Erez-Rosen metric.

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References

  1. Weyl, H. (1917).Ann. Phys. (Leipzig),54, 117.

    Google Scholar 

  2. Chazy, J. (1924).Bull. Soc. Math. France,52, 17.

    Google Scholar 

  3. Curzon, H. E. J. (1924).Proc. London Math. Soc.,23, 477.

    Google Scholar 

  4. Waylen, P. C. (1982).Proc. Roy. Soc. London,A382, 467.

    Google Scholar 

  5. Erez, G. and Rosen, N. (1959).Bull. Res. Counc. of Israel,8F, 47.

    Google Scholar 

  6. Gutsunaev, Ts. I. and Manko, V. S. (1985).Gen. Rel. Grav.,17, 1025.

    Google Scholar 

  7. Geroch, R. (1970).J. Math. Phys.,11, 1955.

    Google Scholar 

  8. Geroch, R. (1970).J. Math. Phys.,11, 2580.

    Google Scholar 

  9. Hansen, R. O. (1974).J. Math. Phys.,15, 46.

    Google Scholar 

  10. Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. G. (1953).Higher Transcendental functions (Univ. of Chicago Press, Chicago).

    Google Scholar 

  11. Doroshkevich, A. G., Zeldovich, Ya. B., and Novikov, I. D. (1965).Zh. Eksp. Teor. Fiz.,67, 433. (1966).Sov. Phys. JETP,22, 122.

    Google Scholar 

  12. Hearn, A. C. (1985). REDUCE 3.2User's Manual (The Rand Corporation, Santa Monica, California).

    Google Scholar 

  13. Kramer, D., Stephani, H., Herlt, E., and MacCallum, M. A. H. (1980).Exact Solutions of Einstein's Field Equations (VEB Deutscher Verlag der Wissenschaften, Berlin).

    Google Scholar 

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

    Google Scholar 

  15. Ehlers, J. (1981). InGrundlagenprobleme der Modernen Physik, J. Nitsch, J. Pfarr, and E.-W. Stachow, eds. (Wissenschaftsverlag, Mannheim).

    Google Scholar 

  16. Quevedo, H. (1986).Phys. Rev. D,33, 334.

    Google Scholar 

  17. Quevedo, H., to be submitted toPhys. Rev. D.

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Quevedo, H. On the exterior gravitational field of a mass with a multipole moment. Gen Relat Gravit 19, 1013–1023 (1987). https://doi.org/10.1007/BF00759580

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