Bilge A.H.Daghan D.2019-08-012019-08-0120089.78276E+121633-4760https://dx.doi.org/10.1051/eas:0830055https://hdl.handle.net/11480/1126Locally 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.eninfo:eu-repo/semantics/closedAccessArticle3032933210.1051/eas:08300552-s2.0-53349102366Q3