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Warped Product Metrics withRank-1 Ricci Tensor

Published online by Cambridge University Press:  30 September 2008

A. Oscoz ,
E. Mediavilla ,
M. Serra-Ricart ,
A.H. Bilge  and
D. Daghan
A.H. Bilge
Affiliation:
Mathematics Engineering Department, Istanbul Technical University, Faculty of Science and Letters, Maslak, 34469 Istanbul, Turkey
D. Daghan
Affiliation:
Mathematics Engineering Department, Istanbul Technical University, Faculty of Science and Letters, Maslak, 34469 Istanbul, Turkey Department of Mathematics, Faculty of Sciences and Letters, Nigde University, Nigde, Turkey
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Abstract

Locally 2+2 warped product metrics with a Lorentzian base andRiemannian fiber are described in Newman-Penrose formalism. Itis shown that solutions with rank-1 Ricci tensor arecharacterized by Φ11 + 3Λ = 0 and Φ00Φ22 = (Φ11-3Λ)2. Integrabilityconditions for the Bianchi identities are studied and it isproved that the sources are null Einstein-Maxwell fields,massless scalar fields or stiff matter fields correspondingrespectively to Λ = 0, Λ > 0 or Λ < 0.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 30: Spanish Relativity Meeting - Encuentros Relativistas Españoles, ERE2007: Relativistic Astrophysics and Cosmology , 2008 , pp. 329 - 332
Copyright
© EAS, EDP Sciences, 2008

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References

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