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

Joan Josep Ferrando Juan Antonio Sáez
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Abstract

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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Joan Josep Ferrando Juan Antonio Sáez. 2007-02-28. On the space-times admitting two shear-free geodesic null congruences. https://doi.org/10.1007/s10714-006-0388-9

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