General Relativity and Gravitation

, Volume 15, Issue 2, pp 105–109 | Cite as

Stationary axisymmetric space-times: A new approach

  • R. S. Ward
Research Articles


This essay describes a new approach to the problem of understanding stationary axisymmetric solutions of Einstein's vacuum equations, different from the “Bäcklund transformation” approach which has recently been extensively developed. It translates the problem into one of complex geometry, using the machinery of twistor theory. This, in turn, leads to a procedure which, in principle, generates all solutions. Some explicit examples are presented.


Differential Geometry Complex Geometry Twistor Theory Vacuum Equation Axisymmetric Solution 
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.
    Geroch, R. (1972).J. Math. Phys.,13, 394.Google Scholar
  2. 2.
    Hauser, I., and Ernst, F. J. (1981).J. Math. Phys.,22, 1051.Google Scholar
  3. 3.
    Maison, D. (1979).J. Math. Phys.,20, 871; Cosgrove, C. M. (1980).J. Math. Phys.,21, 2417; Neugebauer, G., and Kramer, D. (1981).Gen. Rel. Grav.,13, 195.Google Scholar
  4. 4.
    Penrose, R. (1976).Gen. Rel. Grav.,7, 31.Google Scholar
  5. 5.
    Penrose, R. (1975). InQuantum Gravity, eds. C. J. Isham, R. Penrose, and D. W. Sciama, Clarendon Press, Oxford.Google Scholar
  6. 6.
    Witten, L. (1979).Phys. Rev. D,19, 718.Google Scholar
  7. 7.
    Ward, R. S. (1977).Phys. Lett. A,61, 81.Google Scholar
  8. 8.
    Harrison, B. K. (1980).Phys. Rev. D,21, 1695.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • R. S. Ward
    • 1
  1. 1.Institute for Theoretical PhysicsState University of New York at Stony BrookStony Brook

Personalised recommendations