General Relativity and Gravitation

, Volume 20, Issue 10, pp 1067–1081 | Cite as

New series of asymptotically flat axisymmetric and stationary gravitational solutions

  • E. Kyriakopoulos
Research Articles


The equations for the pseudopotential of Harrison's Bäcklund transformations with seed solution an asymptotically flat solution of the Ernst equation are solved. A new series of asymptotically flat solutions of the equations of general relativity is obtained from the determinants of matrices, whose elements are known. The first solution of the series is calculated as a ratio of two sums of monomials. This solution has five arbitrary real constants. For a particular choice of the constants it becomes Kerr's solution.


General Relativity Differential Geometry Real Constant Seed Solution Arbitrary Real Constant 
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  1. 1.
    Geroch, R. (1971).J. Math. Phys.,12, 918; (1972).13, 394.Google Scholar
  2. 2.
    Kinnersley, W. (1977).J. Math. Phys.,18, 1529.Google Scholar
  3. 3.
    Kinnersley, W. and Chitre, D. M. (1977).J. Math. Phys.,18, 1538; (1978).19, 1926; (1978).19, 2037.Google Scholar
  4. 4.
    Cosgrove, C. M. (1977).J. Phys. A,10, 1481; (1977).10, 2093.Google Scholar
  5. 5.
    Hoenselaers, C., Kinnersley, W., and Xanthopoulos, B. C. (1979).J. Math. Phys.,20, 2530.Google Scholar
  6. 6.
    Hauser, I. and Ernst, F. J. (1979).Phys. Rev. D,20, 362; (1979).20, 1783.Google Scholar
  7. 7.
    Kyriakopoulos, E. (1984).Phys. Rev. D,30, 1158.Google Scholar
  8. 8.
    Belinski, V. A., and Zakharov, V. E. (1978).Zh. Eksp. Teor. Fiz.,75, 1958; (1978). [Sov. Phys. JETP,48, 985]; (1979).Zh. Eksp. Teor. Fiz.,77, 3 (1979). [Sou.Phys. JETP,50, 1.].Google Scholar
  9. 9.
    Kramer, D. and Neugebauer, G. (1968).Commun. Math. Phys.,10, 132.Google Scholar
  10. 10.
    Harrison, B. K. (1978).Phys. Rev. Lett.,41, 1197; (1980).Phys. Rev. D,21, 1695.Google Scholar
  11. 11.
    Neugebauer, G. (1979).J. Phys. A,12, L67.Google Scholar
  12. 12.
    Chinea, F. J. (1983).Phys. Rev. Lett.,50, 221.Google Scholar
  13. 13.
    Cosgrove, C. M. (1980).J. Math. Phys.,21, 2417; (1981).22, 2624.Google Scholar
  14. 14.
    Cosgrove, C. M. InProceedings of the Second Marcel Grossmann Meeting on the Recent Developments of General Relativity, Trieste, Italy, July 5–11, 1979, R. Ruffini, ed. (North-Holland, Amsterdam).Google Scholar
  15. 15.
    Neugebauer, G. (1980).J. Phys. A: Math. Gen.,13, L19; (1980).13, 1737.Google Scholar
  16. 16.
    Ernst, F. J. (1968).Phys. Rev.,167, 1175.Google Scholar
  17. 17.
    Kerr, R. P. (1963).Phys. Rev. Lett.,11, 237.Google Scholar
  18. 18.
    Kramer, D., Stephani, H., Herlt, E., and MacCallum, M. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, London).Google Scholar
  19. 19.
    Kinnersley, W., and Kelly, E. F. (1974).J. Math. Phys.,15, 2121.Google Scholar
  20. 20.
    Ehlers, J. (1957). Dissertation, University of Hamburg.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • E. Kyriakopoulos
    • 1
  1. 1.Department of PhysicsNational Technical University of AthensAthensGreece

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