2006/06/30 by Joan Josep Ferrando Juan Antonio Sáez · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1007/s10714-006-0388-9
published as Gen.Rel.Grav.39:343-359,2007 · 18 pages; v2: minor changes
arxiv created 2007/02/28 · arxiv updated 2009/12/01
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.