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General Relativity and Gravitation

, Volume 23, Issue 4, pp 477–486 | Cite as

Reduction of Einstein's field equations for twisting typeN-vacuum fields with anH2

  • Eduard Herlt
Research Articles

Abstract

The problem of vacuum typeN solutions of Einstein's field equations with Killing vector and homothetic group can be reduced to a single ordinary differential equation of the third order for a single real function. Hauser's solution [4] is an exceptional case. If the homothetic parameterN takes the valueN=2 the third order differential equation becomes surprisingly simple. This caseN=2 is therefore the most promising one for the search of exact solutions.

Keywords

Differential Equation Exact Solution Ordinary Differential Equation Field Equation Differential Geometry 
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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References

  1. 1.
    McIntosh, C. B. G. (1985).Class. Quant. Grav.,2, 87.Google Scholar
  2. 2.
    Kramer, D., Stephani, H., MacCallum, M., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).Google Scholar
  3. 3.
    Herlt, B. (1986).Wiss. Zeitschr. der Fr.-Schiller-Universität, Naturwiss. Reihe,35, 735.Google Scholar
  4. 4.
    Hauser, I. (1974).Phys. Rev. Lett.,33, 1112.Google Scholar
  5. 5.
    Chinea, F. J. (1988).Phys. Rev. D,37, 3080.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Eduard Herlt
    • 1
  1. 1.Theoretisch-Physikalisches InstitutFriedrich-Schiller-Universität JenaJenaGermany

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