## Abstract

The aim of this paper is to investigate some geometric and physical properties of the generalized quasi Einstein spacetime G(QE)_{4} under certain conditions. Firstly, we prove the existence of G(QE)_{4} by constructing a non trivial example. Then it is proved that the G(QE)_{4} spacetime with the conditions ℬ⋅S=LSQ(g,S)$\mathcal {B}\cdot S=L_{S}Q(g,S)$, where ℬ$\mathcal {B}$ denotes the Ricci tensor or the concircular curvature tensor is an N(a−b3)$N(\frac {a-b}{3})$-quasi Einstein spacetime and in a G(QE)_{4} spacetime with C ⋅ S = 0, where C is the conformal curvature tensor, a − b is an eigenvalue of the Ricci operator. Then, we deal with the Ricci recurrent G(QE)_{4} spacetime and prove that in this spacetime, the acceleration vector and the vorticity tensor vanish; but this spacetime has the non-vanishing expansion scalar and the shear tensor. Moreover, it is shown that every Ricci recurrent G(QE)_{4} is Weyl compatible, purely electric spacetime and its possible Petrov types are I or D.

Original language | English |
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Pages (from-to) | 548-562 |

Number of pages | 15 |

Journal | International Journal of Theoretical Physics |

Volume | 55 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2016 |

### Bibliographical note

Publisher Copyright:© 2015, Springer Science+Business Media New York.

### Funding

This work which is a part of the first author’s doctoral thesis is supported by Istanbul Technical University. The authors would like to thank the referees for the careful review and the valuable comments.

Funders | Funder number |
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Istanbul Teknik Üniversitesi |

## Keywords

- Generalized quasi Einstein spacetime
- Petrov types
- Purely electric spacetimes
- Ricci recurrent
- Weyl compatibility