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International Journal of Theoretical Physics

, Volume 51, Issue 9, pp 2878–2887 | Cite as

On Conformally Flat Almost Pseudo-Ricci Symmetric Spacetimes

  • Avik De
  • Cihan ÖzgürEmail author
  • Uday Chand De
Article

Abstract

We consider a conformally flat almost pseudo-Ricci symmetric spacetime. At first we show that a conformally flat almost pseudo-Ricci symmetric spacetime can be taken as a model of the perfect fluid spacetime in general relativity and cosmology. Next we show that if in a conformally flat almost pseudo-Ricci symmetric spacetime the matter distribution is perfect fluid whose velocity vector is the vector field corresponding to 1-form B of the spacetime, the energy density and the isotropic pressure are not constants. We also show that a conformally flat almost pseudo-Ricci symmetric spacetime is the Robertson-Walker spacetime. Finally we give an example of a conformally flat almost pseudo-Ricci symmetric spacetime with non-zero non-constant scalar curvature admitting a concircular vector field.

Keywords

Almost pseudo-Ricci symmetric manifold Perfect fluid space time Quasi-Einstein manifold Robertson-Walker spacetime 

Notes

Acknowledgement

The authors wish to express their sincere thanks and gratitude to the referee for his valuable suggestions towards the improvement of the paper.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of CalcuttaKolkataIndia
  2. 2.Department of MathematicsBalikesir UniversityBalikesirTurkey

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