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
Weyl, H. (1917).Ann. Phys. (Leipzig),54, 117.
Chazy, J. (1924).Bull. Soc. Math. France,52, 17.
Curzon, H. E. J. (1924).Proc. London Math. Soc.,23, 477.
Waylen, P. C. (1982).Proc. Roy. Soc. London,A382, 467.
Erez, G. and Rosen, N. (1959).Bull. Res. Counc. of Israel,8F, 47.
Gutsunaev, Ts. I. and Manko, V. S. (1985).Gen. Rel. Grav.,17, 1025.
Geroch, R. (1970).J. Math. Phys.,11, 1955.
Geroch, R. (1970).J. Math. Phys.,11, 2580.
Hansen, R. O. (1974).J. Math. Phys.,15, 46.
Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. G. (1953).Higher Transcendental functions (Univ. of Chicago Press, Chicago).
Doroshkevich, A. G., Zeldovich, Ya. B., and Novikov, I. D. (1965).Zh. Eksp. Teor. Fiz.,67, 433. (1966).Sov. Phys. JETP,22, 122.
Hearn, A. C. (1985). REDUCE 3.2User's Manual (The Rand Corporation, Santa Monica, California).
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).
Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation (W. H. Freeman, San Francisco).
Ehlers, J. (1981). InGrundlagenprobleme der Modernen Physik, J. Nitsch, J. Pfarr, and E.-W. Stachow, eds. (Wissenschaftsverlag, Mannheim).
Quevedo, H. (1986).Phys. Rev. D,33, 334.
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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DOI: https://doi.org/10.1007/BF00759580