Skip to main content
SpringerLink
Log in

HKK transfornatlons: Some results

  • Conference paper
  • First Online:
Solutions of Einstein's Equations: Techniques and Results

Part of the book series: Lecture Notes in Physics ((LNP,volume 205))

Abstract

We simgify considerably the original representation of the HKX transformations by means of determinants. We present some examples to illustrate the action of these transformations. We show the equivalence of HKX and Kramer-Neugebauer transformations. Finally, we sketch the analysis of two balancing Kerr-NUT objects.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

Chapter I

  1. H. Weyl, Ann. Phys. 54, 117 (1917)

    Google Scholar 

  2. R.P. Kerr, Phys. Rev. Lett. 11, 237 (1963)

    Google Scholar 

  3. F.J. Ernst, Phys. Rev. 167, 1175 (1968)

    Google Scholar 

  4. A. Tomimatsu, H. Sato, Phys. Rev. Lett. 29, 1344 (1972) and Prog. Theor. Phys. 50, 95 (1973)

    Google Scholar 

  5. G. Neugebauer, Phys. Lett. 75A, 259 (1980)

    Google Scholar 

  6. V.A. Belinsky, V.A. Zakharov, JEPT, 50, 1, (1979)

    Google Scholar 

  7. B.K. Harrison, Phys. Rev. D 21, 1965 (1980)

    Google Scholar 

  8. C.M. Cosgrove, J. Phys. A 11, 2405 (1978)

    Google Scholar 

  9. I. Hauser, F.J. Ernst, J. Math. Phys. 21, 1126 (1980)

    Google Scholar 

  10. W. Kinnersley, J. Math. Phys. 14, 651 (1973)

    Google Scholar 

  11. W. Kinnersley, J. Math. Phys. 18, 1529 (1977)

    Google Scholar 

  12. W. Kinnersley, D. Chitre, J. Math. Phys. 18, 1538 (1977)

    Google Scholar 

  13. W. Kinnersley, D. Chitre, J. Math. Phys. 19, 1926 (1978)

    Google Scholar 

  14. W. Kinnersley, D. Chitre, J. Math. Phys. 19, 2037 (1978)

    Google Scholar 

  15. C. Hoenselaers, W. Kinnersley and B. Xanthopoulos, J. Math. Phys. 20, 2530 (1979)

    Google Scholar 

  16. T. Lewis, Proc. Roy. Soc. Lond. A 136, 176 (1932)

    Google Scholar 

  17. D.M. Zipoy, J. Math. Phys. 7, 1137 (1966)

    Google Scholar 

  18. B. Voorhees, Phys. Rev. D2, 2119 (1970)

    Google Scholar 

  19. K. Schwarzschild, Sitz. PreuB. Akad. Wiss. 189 (1916)

    Google Scholar 

  20. R. Bach, H. Weyl, Math. Z. 13, 134 (1922)

    Google Scholar 

  21. J. Chazy, Bull. Soc. Math. France 52, 17 (1924)

    Google Scholar 

  22. H.E.J. Curzon, Proc. London Math. Soc. 23, 477 (1924)

    Google Scholar 

  23. J. L. Synge, Relativity: The General Theory, Amsterdam 1971, pp. 314

    Google Scholar 

  24. W. Israel, Phys. Rev. D15, 937 (1977)

    Google Scholar 

Chapter II

  1. W. Dietz, Gen. Rel. Grav. 15, 911 (1983)

    Google Scholar 

  2. W. Dietz, Gen. Rel. Grav. 16, 249 (1984)

    Google Scholar 

  3. C. Cosgrove, J. Math. Phys. 21, 2417 (1980)

    Google Scholar 

  4. C. Hoenselaers and W. Dietz, Gen. Rel. Grav. 16, 71 (1984)

    Google Scholar 

Chapter III

  1. C. Hoenselaers, W. Kinnersley and B. Xanthopoulos, J. Math. Phys. 20, 2530 (1979)

    Google Scholar 

  2. W. Dietz, C. Hoenselaers, Proc. R. Soc. Lond. A 382, 221 (1982)

    Google Scholar 

  3. W. Dietz, C. Hoenselaers, Phys. Rev. Lett. 48, 778 (1982)

    Google Scholar 

  4. D. Kramer, in this volume

    Google Scholar 

  5. D. Kramer, G. Neugebauer, Phys. Lett. u75A, 259 (1980)

    Google Scholar 

  6. M. Yamazaki, in this volume

    Google Scholar 

  7. M. Yamazaki, Prog. Theor. Phys. 68, 503 (1983)

    Google Scholar 

  8. K. Oohara, H. Sato, Prog. Theor. Phys. 65, 1891 (1981)

    Google Scholar 

  9. W. Dietz, “On Techniques for Generating Solutions and Generated Two Mass Solutions of Einstein's Vacuum Equations”, Habilitationsschrift, Universität Würzburg (1984)

    Google Scholar 

  10. W. Dietz, C. Hoenselaers, in preparation

    Google Scholar 

  11. W. Kinnersley, D.M. Chitre, J. Math. Phys. 19, 2037 (1978)

    Google Scholar 

  12. C. Hoenselaers, “Remarks on the double Kerr solution”, submitted to Prog. Theor. Phys.

    Google Scholar 

  13. C. Cosgrove, J. Math. Phys. 21, 2417 (1980)

    Google Scholar 

  14. C. Hoenselaers, “Axisymmetric Stationary Vacuum Solutions of Einstein's Equations”, Habilitationsschrift, Universität München (1982)

    Google Scholar 

Chapter IV

  1. W. Dietz and C. Hoenselaers, Phys. Rev. Lett. 48, 778 (1982)

    Google Scholar 

  2. W. Israel, Phys. Rev. D 15, 937 (1977)

    Google Scholar 

  3. W. Dietz, “On Techniques for Generating Solutions and Generated Two Mass Solutions of Einstein's Vacuum Equations”, Habilitationschrift, Universität Würzburg (1984)

    Google Scholar 

  4. W. Dietz, C. Hoenselaers, in preparation

    Google Scholar 

  5. Landolt-Börnstein, Zahlenwerte und Funktionen aus Naturwissenschaft und Technik, N Neue Serie, Gruppe VI, Band 1, Berlin (1965)

    Google Scholar 

  6. H.-H. Voigt, Abriss der Astronomie, Mannheim (1969) *** DIRECT SUPPORT *** A3418162 00003

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Astronomie und Astrophysik, Am Hubland, D-8700, Würzburg, Germany

    Werner Dietz

Authors
  1. Werner Dietz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

C. Hoenselaers W. Dietz

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Dietz, W. (1984). HKK transfornatlons: Some results. In: Hoenselaers, C., Dietz, W. (eds) Solutions of Einstein's Equations: Techniques and Results. Lecture Notes in Physics, vol 205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13366-6_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-13366-6_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13366-7

  • Online ISBN: 978-3-540-38922-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation