General Relativity and Gravitation

, Volume 7, Issue 10, pp 817–838 | Cite as

Axisymmetric gravitational fields

  • C. Reina
  • A. Treves
Review Article


In this review paper Einstein equations for axisymmetric vacuum fields are introduced in the form given by Lewis. Following Ernst they are reduced to one complex potential equation. Weyl-type, Schwarzschild, Kerr, Tomimatsu-Sato solutions, and their NUT-like generalizations are then discussed.


Differential Geometry Gravitational Field Einstein Equation Review Paper Potential Equation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schwarzschild, K. (1916).Sitzungsber. Preuss. Akad. Wiss.,189.Google Scholar
  2. 2.
    Israel, W. (1967).Phys. Rev.,164, 1776.Google Scholar
  3. 3.
    Weyl, H. (1917).Ann. Phys. Leipzig,54, 117.Google Scholar
  4. 4.
    Levi Civita, T. (1917).Atti Accad. Naz. Lincei,5, 26.Google Scholar
  5. 5.
    Safko, J. L., and Witten, L. (1971).J. Math. Phys.,12, 257.Google Scholar
  6. 6.
    Lewis, T. (1932).Proc. R. Soc. (London) A136, 176.Google Scholar
  7. 7.
    Van Stockum, W. J. (1937).Proc. R. Soc. Edinburgh,57, 135.Google Scholar
  8. 8.
    Kerr, R. P. (1963).Phys. Rev. Lett.,11, 237.Google Scholar
  9. 9.
    Tomimatsu, A., and Sato, H. (1972).Phys. Rev. Lett.,29, 1344.Google Scholar
  10. 10.
    Reissner, H. (1916).Ann. Phys. Leipzig,50, 106.Google Scholar
  11. 11.
    Nordstrom, G. (1918).Verh. K. Ned. Akad. Wet. Afd., Natuurkd.,26, 1201.Google Scholar
  12. 12.
    Weyl, H. (1922).Space-Time-Matter (Methuen, London).Google Scholar
  13. 13.
    Newman, E. T., Couch, E., Chinnapared, K., Exton, A., Prakash, A., and Torrence, R. (1965).J. Math. Phys.,6, 918.Google Scholar
  14. 14.
    Ernst, F. J. (1913).Phys. Rev. D,7, 2520.Google Scholar
  15. 15.
    Newman, E. T., Tamburino, L., and Unti, T. (1963).J. Math. Phys.,4, 915.Google Scholar
  16. 16.
    Demianski, M., and Newman, E. T. (1966).Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys.,14, 653.Google Scholar
  17. 17.
    Carter, B. (1975).Marcel Grossmann Meetings Proceedings (ed. Ruffini, R.) North Holland, Amsterdam (in press).Google Scholar
  18. 18.
    Ehlers, J. (1959).Les theories relativistes de la gravitation (CNRS, Paris).Google Scholar
  19. 19.
    Carter, B. (1968).Comm. Math. Phys.,10, 280.Google Scholar
  20. 20.
    Ernst, F. J. (1968).Phys. Rev.,167, 1175.Google Scholar
  21. 21.
    Ernst, F. J. (1968).Phys. Rev.,168, 1415.Google Scholar
  22. 22.
    Ernst, F. J. (1974).J. Math. Phys.,15, 1409.Google Scholar
  23. 23.
    Harrison, B. K. (1968).J. Math. Phys.,9, 1744.Google Scholar
  24. 24.
    Geroch, R. (1971).J. Math. Phys.,12, 918.Google Scholar
  25. 25.
    Israel, W., and Wilson, G. A. (1972).J. Math. Phys.,13, 865.Google Scholar
  26. 26.
    Kinnersley, W. (1973).J. Math. Phys.,14, 651.Google Scholar
  27. 27.
    Plebanski, J. F. (1975).Ann. Phys. N.Y.,90, 196.Google Scholar
  28. 28.
    Carter, B. (1972). inBlack Holes, (eds. DeWitt, C. and DeWitt, B. S.) Gordon and Breach, New York.Google Scholar
  29. 29.
    Debney, G., Kerr, R. P., and Schild, A. (1969).J. Math. Phys.,10, 1842.Google Scholar
  30. 30.
    Papapetrou, A. (1953).Ann. Phys.,12, 309.Google Scholar
  31. 31.
    Sato, H. (1975).Proc. Enrico Fermi School 65.Google Scholar
  32. 32.
    Synge, J. L. (1966).Relativity, The General Theory (North Holland, Amsterdam).Google Scholar
  33. 33.
    Landau, L., and Lifschitz, E. (1966).Theorie des Champs (MIR, Moscow).Google Scholar
  34. 34.
    Tomimatsu, A., and Sato, H. (1973).Prog. Theor. Phys.,50, 95.Google Scholar
  35. 35.
    Zipoy, D. M. (1966).J. Math. Phys.,7, 1137.Google Scholar
  36. 36.
    Voorhers, B. H. (1910).Phys. Rev. D2, 2119.Google Scholar
  37. 37.
    Morse, P. M., and Feshbach, H. (1953).Methods of Theoretical Physics (McGraw Hill, New York).Google Scholar
  38. 38.
    Bell, L. (1971).Gen. Rel Grav.,1, 337.Google Scholar
  39. 39.
    Boyer, R. H., and Lindquist, R. W. (1967).J. Math. Phys.,8, 265.Google Scholar
  40. 40.
    Reina, C., and Treves, A. (1975).J. Math. Phys.,16, 834.Google Scholar
  41. 41.
    Levy, H. (1968).Nuovo Cimento,56B, 253.Google Scholar
  42. 42.
    Chandrasekhar, S., and Friedman, J. L. (1972).Ap. J.,175, 379.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • C. Reina
    • 1
  • A. Treves
    • 1
  1. 1.Istituto di Fisica dell'Università and Laboratorio di Fisica Cosmica e Tecnologie Relative del C.N.R.Milano

Personalised recommendations