General Relativity and Gravitation

, Volume 7, Issue 10, pp 809–815 | Cite as

On the existence of a general rotating solution of Einstein's equations

  • Jamal N. Islam
Research Articles

Abstract

In an earlier paper we considered a power-series expansion of the metric for a rotating field in terms of a parameter and constructed a solution of Einstein's equations to the first few orders in terms of two harmonic functions. We encountered a pair of Poisson-type equations which were apparently insoluble explicitly. The form of the metric considered was the Weyl-Lewis-Papapetrou form. In this paper we consider a power-series expansion of the most general form of a rotating metric and show that one encounters the same two Poisson equations as before. If these equations are insoluble explicitly, as seems likely, then a general solution depending on two harmonic functions cannot exist in closed form.

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References

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    For a review of rotating solutions, see, e.g., Thorne, K. S. (1971). inGravitation and Cosmology, Proceedings of the International School of Physics Enrico Fermi Course 47 ed. Sachs, R. K. (Academic Press, New York); or Carter, B., and Bardeen, J. M. (1972). inBlack Holes, Proceedings of the Les Hauches Summer School ed. DeWitt, C., and DeWitt, B. S. (Gordon and Breach, New York).Google Scholar
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    Islam, J. N. (1976).Math. Proc. Cambridge Phil. Soc.,79, 161.Google Scholar
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    Lewis, T. (1932).Proc. R. Soc. London,A136, 176.Google Scholar
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    Papapetrou, A. (1953).Ann. Phys. Leipzig,12, 309.Google Scholar
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    Tomimatsu, A., and Sato, H. (1973).Prog. Theor. Phys. (Kyoto),50, 95.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Jamal N. Islam
    • 1
  1. 1.Department of Applied Mathematics and AstronomyUniversity CollegeCardiffUK

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