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

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.

18 pages; v2: minor changes

References in corpus (3)

• A Rainich-like approach to the Killing-Yano tensors
• On the classification of type D spacetimes
• On the geometry of Killing and conformal tensors

Cited by in corpus (6)

• On the invariant symmetries of the $\mathcal{D}$-metrics
• Killing-Yano Tensors of Order n-1
• Rainich theory for type D aligned Einstein-Maxwell solutions
• Type D vacuum solutions: a new intrinsic approach
• Foliation-generating observers under Lorentz transformations
• Two special classes of space-times admitting a non-null valence two Killing spinor