WARPED PRODUCT METRICS WITH RANK-1 RICCI TENSOR


Bilge A. H. , Daghan D.

30th Spanish Relativity Conference, Tenerife, Spain, 10 - 14 September 2007, vol.30, pp.329-332 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 30
  • Doi Number: 10.1051/eas:0830055
  • City: Tenerife
  • Country: Spain
  • Page Numbers: pp.329-332

Abstract

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-1 Ricci tensor are characterized by Phi(11) + 3 Lambda = 0 and Phi(00)Phi(22) = (Phi(11) - 3 Lambda)(2). 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 Lambda = 0, Lambda > 0 or Lambda < 0.