International Journal of Theoretical Physics

, Volume 10, Issue 4, pp 217–227 | Cite as

Classification of stationary space-times

  • Zoltán Perjés
Article

Abstract

A systematic approach to the geometric structure of stationary gravitational fields is presented. The algebraic type of the trace-free Ricci tensor together with the propagation properties of the eigenrays in the background 3-space defined by the Killing trajectories serve as a basis for classifying the solutions of the stationary field equations. The eigenrays are the integral curves belonging to the solutions ξA of the eigenvalue problemG A B ξB=μξA,G A B spinor representing the gravitational field in the background space. Many of the already known stationary metrics can be derived in the present scheme but new solutions of the field equations are also obtained. The possible types of the vacuum and electrovac fields are discussed in their connection with the corresponding exact solutions.

Keywords

Field Theory Exact Solution Quantum Field Theory Stationary Field Systematic Approach 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Перов, А. З. (1966). Новьге методьг в общей теории относительности. (Nauka, Moscow).Google Scholar
  2. Bonnor, W. (1966).Zeitschrift für Physik 190 444.Google Scholar
  3. Geroch, R. (1971).Journal of Mathematical Physics 12, 918.Google Scholar
  4. Infeld, L. and van der Waerden, B. L. (1933).Sitzungsberichte der Preussischen Academie der Wissenschaften zu Berlin 9 380.Google Scholar
  5. Israel, W. and Wilson, G. A. (1972).Journal of Mathematical Physics 13 865.Google Scholar
  6. Kóta, J. and Perjés, Z. (1972).Journal of Mathematical Physics 13 1695.Google Scholar
  7. Lukács, B. (1973). To be published.Google Scholar
  8. Lukács, B. and Perjés, Z. (1973). General Relativity & Gravitation,4 161.Google Scholar
  9. Papapetrou, A. (1953).Annaler der Physik 12 309.Google Scholar
  10. Penrose, R. (1960).Annals of Physics 10 171.Google Scholar
  11. Perjés, Z. (1969).Communications in Mathematical Physics 12 275.Google Scholar
  12. Perjés, Z. (1970).Journal of Mathematical Physics 11 3383.Google Scholar
  13. Perjés, Z. (1971a). Thesis, Central Res. Inst. Phys., Budapest (unpublished).Google Scholar
  14. Perjés, Z. (1971b).Physical Review Letters 27 1668.Google Scholar
  15. Perjés, Z. (1972).Acta Physica Academiae Scientiarum Hungaricae 32 207.Google Scholar
  16. Pirani, F. A. E. (1964).Lectures on General Relativity. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
  17. Smorodinski, J. A. (1965).Soviet Physics: Uspekhi 7 637.Google Scholar
  18. Synge, J. L. (1960).The General Relativity. North-Holland Publishing Co.Google Scholar
  19. Weyl, H. (1917).Annalen der Physik 54 117.Google Scholar

Copyright information

© Plenum Publishing Company Limited 1974

Authors and Affiliations

  • Zoltán Perjés
    • 1
  1. 1.Department of Mathematics, Birkbeck CollegeUniversity of LondonUK

Personalised recommendations