Effective connections and fields associated with shear-free null congruences

Details Effective connections and fields associated with shear-free null congruences Effective connections and fields associated with shear-free null congruences

2004-01-29

arxiv.org/abs/gr-qc/0401120v1

Gen.Rel.Grav. 36 (2004) 1603-1612

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, talk presented on the Third Ulyanovsk International School-Seminar UISS-2003 "Problems of Theoretical and Observatio

Scientific paper

10.1023/B:GERG.0000032152.79799.

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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