A nonstationary generalization of the Kerr congruence

Vladimir V. Kassandrov1


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 a necessary (ëlementary") unit.


  1. G. C. Debney, R. P. Kerr and A. Schild, J. Math. Phys. 10, 1842 (1969).
  2. R. Penrose and W. Rindler, Spinors and Space-Time, Vol. II (Cambridge Univ. Press, Cambridge, 1986).
  3. V. V. Kassandrov and J. A. Rizkallah, Twistor and "Weak" Gauge Structures in the Framework of Quaternionic Analysis, gr-qc/ 0012109.
  4. V. V. Kassandrov, in: Space-Time Structure. Algebra and Geometry (ed. D. G. Pavlov et al., Lilia-Print, Moscow, 2007, p. 441, arXiv: 0710.2895).
  5. V. V. Kassandrov, Algebraic Structure of Space-Time and Algebrodynamics (People Fried. Univ. Press, 1992, in Russian).
  6. V. V. Kassandrov, Grav. Cosmol 3, 216 (1995); gr-qc/0007026.
  7. G. F. Torres del Castillo, Gen. Rel. Grav. 31, 205 (1999).
  8. V. V. Kassandrov and V. N. Trishin, Gen. Rel. Grav. 36, 1603, (2004), gr-qc/0411120.
  9. V.V. Kassandrov and J.A. Rizcallah, in: Recent Problems in Field Theory (ed. A.V. Aminova, Kasan Univ. Press, Kasan, 1998, p. 176; gr-qc/9809078).
  10. I. Robinson, J. Math. Phys. 2, 290 (1961).
  11. W. Kinnersley, Phys. Rev. 186, 1335 (1969).
  12. M. Gurses, F. Gursey, J. Math. Phys. 16, 2385 (1974).
  13. R. W. Lind and E. T. Newman, J. Math. Phys. 15, 1103 (1974).
  14. E. T. Newman and J. Winicour, J. Math. Phys. 15, 1113 (1974).
  15. V. V. Kassandrov, in: Has the Last Word Been Said on Classical Electrodynamics? (ed. A. Chubykalo et al., Rinton Press, 2004, p. 42, physics/0308045).
  16. V. A. Fock, Theory of Space, Time and Gravitation (Fizmatgiz, Moscow, 1961 (in Russian)).
  17. E. T. Newman, J. Math. Phys., 14, 102 (1973).
  18. V.V. Kassandrov, in: "Proc. Int. Sch. on Geometry and Analysis", Rostov-na-Donu Univ. Press, 2004, p. 65, gr-qc/0602046.
  19. H. Bateman, The Mathematical Analysis of Electrical and Optical Wave-Motion, Dover Publ. Inc., 1955.
  20. B. Carter, Phys. Rev. 174, 1559 (1968).
  21. A. Ya. Burinskii, J. Phys. A: Math. Theor. 41, 164069 (2008); arXiv: 0710.4249.
  22. E. T. Newman, Phys. Rev. D65, 104005 (2002); gr-qc/0201055.
  23. V. V. Kassandrov, Grav. Cosmol. 11, 354 (2005); gr-qc/0602088.
  24. V. V. Kassandrov, in: "Proc. Int. Conf. Phys. Interpret. Rel. Theory (PIRT-2005)", eds. V.O. Gladyshev et al., Bauman Tech. Univ. Press, Moscow, 2005, p. 42, gr-qc/0602064.
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