Gravitation and Cosmology

, Volume 15, Issue 3, pp 213–219 | Cite as

A nonstationary generalization of the Kerr congruence

  • V. V. KassandrovEmail author


Making use of the Kerr theorem for shear-free null congruences and of Newman’s representation for a virtual charge “moving” in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a singular ring uniformly contracting to a point and expanding then to infinity. Electromagnetic and complex eikonal field distributions are naturally associated with the obtained congruence, with electric charge being necessarily unit (“elementary”).

PACS numbers

02.40.Ky 03.50.De 04.20.Cv 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. C. Debney, R. P. Kerr, and A. Schild, J. Math. Phys. 10, 1842 (1969).CrossRefMathSciNetADSGoogle Scholar
  2. 2.
    R. Penrose and W. Rindler, Spinors and Space-Time, Vol. II (Cambridge Univ. Press, Cambridge, 1986).Google Scholar
  3. 3.
    V. V. Kassandrov and J. A. Rizkallah, Twistor and “Weak“ Gauge Structures in the Framework of Quaternionic Analysis, gr-qc/0012109.Google Scholar
  4. 4.
    V. V. Kassandrov, in: Space-Time Structure. Algebra and Geometry, Ed. by D. G. Pavlov et al. (Lilia-Print, Moscow, 2007), p. 441, arXiv: 0710.2895.Google Scholar
  5. 5.
    V. V. Kassandrov, Algebraic Structure of Space-Time and Algebrodynamics (People Fried. Univ. Press, 1992), (in Russian).Google Scholar
  6. 6.
    V. V. Kassandrov, Grav. Cosmol 3, 216 (1995); grqc/0007026.ADSGoogle Scholar
  7. 7.
    G. F. Torres del Castillo, Gen. Rel. Grav. 31, 205 (1999).zbMATHCrossRefMathSciNetADSGoogle Scholar
  8. 8.
    V. V. Kassandrov and V. N. Trishin, Gen. Rel. Grav. 36, 1603, (2004); gr-qc/0411120.zbMATHCrossRefMathSciNetADSGoogle Scholar
  9. 9.
    V.V. Kassandrov and J. A. Rizcallah, in: Recent Problems in Field Theory, Ed. by A. V. Aminova (Kasan Univ. Press, Kasan, 1998), p. 176; gr-qc/9809078.Google Scholar
  10. 10.
    I. Robinson, J.Math. Phys. 2, 290 (1961).CrossRefADSGoogle Scholar
  11. 11.
    W. Kinnersley, Phys. Rev. 186, 1335 (1969).CrossRefMathSciNetADSGoogle Scholar
  12. 12.
    M. G’urses and F. Gúrsey, J. Math. Phys. 16, 2385 (1974).CrossRefGoogle Scholar
  13. 13.
    R. W. Lind and E. T. Newman, J. Math. Phys. 15, 1103 (1974).CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    E. T. Newman and J. Winicour, J. Math. Phys. 15, 1113 (1974).CrossRefMathSciNetADSGoogle Scholar
  15. 15.
    V. V. Kassandrov, in: Has the Last Word Been Said on Classical Electrodynamics? Ed. by A. Chubykalo et al. (Rinton Press, 2004), p. 42; physics/0308045.Google Scholar
  16. 16.
    V. A. Fock, Theory of Space, Time and Gravitation (Fizmatgiz, Moscow, 1961), (in Russian).Google Scholar
  17. 17.
    E. T. Newman, J.Math. Phys. 14, 102 (1973).CrossRefADSGoogle Scholar
  18. 18.
    V. V. Kassandrov, in Proc. Int. Sch. on Geometry and Analysis (Rostov-na-Donu Univ. Press, 2004), p. 65; gr-qc/0602046.Google Scholar
  19. 19.
    H. Bateman, The Mathematical Analysis of Electrical and Optical Wave-Motion (Dover Publ. Inc., 1955).Google Scholar
  20. 20.
    B. Carter, Phys. Rev. 174, 1559 (1968).zbMATHCrossRefADSGoogle Scholar
  21. 21.
    A. Ya. Burinskii, J. Phys. A:Math. Theor. 41, 164 069 (2008); arXiv: 0710.4249.Google Scholar
  22. 22.
    E. T. Newman, Phys. Rev. D 65, 104 005 (2002); grqc/0201055.Google Scholar
  23. 23.
    V. V. Kassandrov, Grav. Cosmol. 11, 354 (2005); grqc/0602088.zbMATHMathSciNetADSGoogle Scholar
  24. 24.
    V. V. Kassandrov, in Proc. Int. Conf. Phys. Interpret. Rel. Theory (PIRT-2005), Ed. by V. O. Gladyshev et al. (Bauman Tech.Univ. Press, Moscow, 2005), p. 42; gr-qc/0602064.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Institute of Gravitation and CosmologyPeoples’ Friendship University of RussiaMoscowRussia

Personalised recommendations