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    Warped product metrics with rank-1 ricci tensor
    (2008) Bilge A.H.; Daghan D.
    Locally 2 + 2 warped product metrics with a Lorentzian base and Riemannian fiber are described in Newman-Penrose formalism. It is shown that solutions with rank- Ricci tensor are characterized by ?11 +3A = 0 and ?00 ?22 =(?11 - 3A)23. Integrability conditions for the Bianchi identities are studied and it is proved that the sources are null Einstein-Maxwell fields, massless scalar fields or stiff matter fields corresponding respectively to = 0, > 0 or < 0. © 2008 EAS EDP Sciences.