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Double complex Bäcklund transformations of the axisymmetric stationary and cylindrical symmetric Einstein vacuum field and a Geroch group structure

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Abstract

Neugebauer's results are doublized and the double complex transformations of the axisymmetric stationary vacuum field and the cylindrically symmetric vacuum field are obtained. Neugebauer's original results correspond to half of ours. By making use of these double Bäcklund transformations, we can construct a kind of double realization of the Geroch group. This cannot be achieved from Neugebauer's original results. Moreover, it is more general than Zhong's.

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References

  1. Ernst, F. J. (1967).Physical Review,167, 1175.

  2. Ernst, F. J. (1968).Physical Review,168, 1415.

  3. Geroch, R. (1971).Journal of Mathematical Physics,12, 918.

  4. Geroch, R. (1972).Journal of Mathematical Physics,13, 132.

  5. Kyriakopoulos, E. (1988).General Relativity and Gravitation,20, 1067.

  6. Letelier, P. S. (1984).Journal of Mathematical Physics,25, 2675.

  7. Neugebauer, G. (1979).Journal of Physics A: Mathematical and General,12, L67.

  8. Zhong, Z. Z. (1985).Journal of Mathematical Physics,26, 2589.

  9. Zhong, Z. Z. (1988).Scientia Sinica A,XXXI, 436.

  10. Zhong, Z. Z. (1989).Journal of Mathematical Physics,30, 1158.

  11. Zhong, Z. Z. (1990a).Journal of Mathematical Physics,31, 2217.

  12. Zhong, Z. Z. (1990b).Science in China (Series A),33, 1089.

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Zhong, H., Zhong, Z. Double complex Bäcklund transformations of the axisymmetric stationary and cylindrical symmetric Einstein vacuum field and a Geroch group structure. Int J Theor Phys 33, 425–434 (1994). https://doi.org/10.1007/BF00844981

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Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Stationary Vacuum
  • Group Structure