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On the structure of general solution to the equations of shear-free null congruences

Vladimir V. Kassandrov
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Abstract

We demonstrate that the source of a shear-free null congruence is, generically, a world sheet of a singular string in the complex Minkowski space. In particular cases the string degenerates into the Newman's point singularity. We describe also a time-dependent deformation of the Kerr's congruence which could indicate the unstability of the Kerr (Kerr-Newman) (electro)vacuum solution. Then we consider a 5D extension of Minkowski space obtained by complexification of the time coordinate. Singular locus of a shear-free null congruence on such an extended space-time consists of a (great) number of point particles (``markeons'') and 2D surfaces -- light-like wave fronts.

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Vladimir V. Kassandrov. 2006-02-13. On the structure of general solution to the equations of shear-free null congruences. https://arxiv.org/abs/gr-qc/0602046

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