Abstract
A special subclass of shear-free null congruences (SFC) is studied, with tangent vector field being a repeated principal null direction of the Weyl tensor. We demonstrate that this field is parallel with respect to an effective affine connection which contains the Weyl nonmetricity and the skew symmetric torsion. On the other hand, a Maxwell-like field can be directly associated with any special SFC, and the electric charge for bounded singularities of this field turns to be “self-quantized.” Two invariant differential operators are introduced which can be thought of as spinor analogues of the Beltrami operators and both nullify the principal spinor of any special SFC.
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REFERENCES
Penrose, R., and Rindler W. (1986/1988). Spinors and Space-Time, Vols. 1 and 2, Oxford University Press, Oxford.
Kinnersley, W. (1969). Phys. Rev. 186, 1335.
Kassandrov, V. V. (2002). Grav. Cosmol, 8 (Suppl. 2), 57.
Kassandrov, V. V. (1998). Acta Appl. Math. 50, 197; Kassandrov, V. V. (1992). The Algebraic Structure of Space-Time and the Algebrodynamics, People's Friendship University Press, Moscow. (in Russian)
Kassandrov, V. V., and Rizcallah J. A. (2000). (e-print gr-qc/0012109).
Kassandrov V. V. (1995). Grav. Cosmol. 1, 216.
Kassandrov, V. V., and Trishin V. N. (1999) Grav. Cosmol 5, 272.
Ward, R. S., and Wells, R. O. (1990). Twistor Geometry and Field Theory, Cambridge University Press, Cambridge.
Robinson, I. (1961). J. Math. Phys. 2, 290.
Benn, I. M., Charlton, P., and Kress, J. (1997). J. Math. Phys. 38, 4504.
Cohen, J. M., and Kegeles, L. S. (1974). Phys. Rev. D 10, 1070; Cohen, J. M., and Kegeles, L. S. (1979). Phys. Rev. D 19, 1641.
Kerr, R. P., and Wilson, W. B. (1979). Gen. Rel. Grav. 10, 273.
Kassandrov, V. V., and Rizcalla J. A. (2002). In Proc.XXVWorkshop on the Fundamental Problems of High Energy Physics and Field Theory, Vol. 199, High Energy Physics Institute Press, Protvino.
Kassandrov, V. V. (2003). (e-print physics/0308045).
Goldberg, J. N., and Sachs, R. K. (1962). Acta Phys. Polon. 22, 13.
Sommers, P. (1976). Proc. R. Soc. Lond. Ser. A 349, 309.
Nurowski, P., and Trautman, A. (2002). (e-print math.DG/0201266).
Krechet, V. G. (1995). Grav. Cosmol 1, 199.
Tod, K. P. (1996). Class. Quant. Grav. 13, 2609.
Dirac, P. A. M. (1931). Proc. R. Soc. Lond. A 133, 60; Dirac, P. A. M. (1948). Phys. Rev. 74, 817.
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Kassandrov, V.V., Trishin, V.N. Effective Connections and Fields Associated with Shear-Free Null Congruences. General Relativity and Gravitation 36, 1603–1612 (2004). https://doi.org/10.1023/B:GERG.0000032152.79799.8a
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DOI: https://doi.org/10.1023/B:GERG.0000032152.79799.8a