On the space-times admitting two shear-free geodesic null congruences

Details On the space-times admitting two shear-free geodesic null congruences On the space-times admitting two shear-free geodesic null congruences

2006-06-02

arxiv.org/abs/gr-qc/0606015v2

Gen.Rel.Grav.39:343-359,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages; v2: minor changes

Scientific paper

10.1007/s10714-006-0388-9

We analyze the space-times admitting two shear-free geodesic null congruences. The integrability conditions are presented in a plain tensorial way as equations on the volume element $U$ of the time-like 2--plane that these directions define. From these we easily deduce significant consequences. We obtain explicit expressions for the Ricci and Weyl tensors in terms of $U$ and its first and second order covariant derivatives. We study the different compatible Petrov-Bel types and give the necessary and sufficient conditions that characterize every type in terms of $U$. The type D case is analyzed in detail and we show that every type D space-time admitting a 2+2 conformal Killing tensor also admits a conformal Killing-Yano tensor.

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