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Soviet Physics Journal

, Volume 16, Issue 11, pp 1572–1576 | Cite as

Use of conformal, mapping to construct new solutions of the Einstein equations

  • A. V. Nosovets
Article
  • 21 Downloads

Abstract

A method is obtained for constructing new solutions of the Einstein equations from known solutions, beginning with the structure of the Einstein tensor and using conformai mapping. The sollowing cases are considered: transformation of vacuum solutions into hydrodynamic solutions and the transformation of hydrodynamic solutions into solutions of the same type. A necessary and sufficient condition, imposed on the vacuum metric, is found which guarantees that solutions with a hydrodynamic energy-momentum tensor will be produced from vacuum solutions.

Keywords

Einstein Equation Vacuum Solution Einstein Tensor Hydrodynamic Solution Conformai Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature cited

  1. 1.
    I. M. Dozmorov, Izv. VUZ SSSR, Fiz., No. 9, 52 (1970).Google Scholar
  2. 2.
    I. Ehlers, Colloq. Internat. Centre Nat. Rech. Scient.,91, 275 (1962).Google Scholar
  3. 3.
    M. M. Kumar, Nuovo Cimento,63, 559 (1969).Google Scholar
  4. 4.
    J. L. Synge, Relativity: The General Theory, North Holland, Amsterdam (1960).Google Scholar
  5. 5.
    K. Yano and S. Bochner, Curvature and Betti Numbers, Princeton University Press, Princeton (1953).Google Scholar
  6. 6.
    G. I. Kruchkovich, Usp. Matem. Nauk,12, No. 6, 153 (1957).Google Scholar
  7. 7.
    G. I. Kruchkovich, “Kagan spaces,” in: V. F. Kagan, Subprojective Spaces [in Russian], Moscow (1961), p. 177.Google Scholar
  8. 8.
    P. K. Rashevskii, Proceedings of the Seminar on Vector and Tensor Analysis [in Russian], No. 1 (1933), p. 126.Google Scholar
  9. 9.
    H. L. de Vries, Math. Zeitschr., No. 3, 328 (1954).Google Scholar
  10. 10.
    A. Z. Petrov, New Methods in the General Theory of Relativity [in Russian], Moscow (1966).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • A. V. Nosovets
    • 1
  1. 1.Kuban State UniversityUSSR

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