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

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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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Authors and Affiliations

  1. Departament d’Astronomia i Astrofísica, Universitat de València, 46100, Burjassot, València, Spain

    Joan Josep Ferrando

  2. Departament de Matemàtiques per a l’Economia i l’Empresa, Universitat de València, 46071, València, Spain

    Juan Antonio Sáez

Authors
  1. Joan Josep Ferrando
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  2. Juan Antonio Sáez
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Correspondence to Joan Josep Ferrando.

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Ferrando, J.J., Sáez, J.A. On the space-times admitting two shear-free geodesic null congruences. Gen Relativ Gravit 39, 343–359 (2007). https://doi.org/10.1007/s10714-006-0388-9

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  • DOI: https://doi.org/10.1007/s10714-006-0388-9

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