Tsukuba Journal of Mathematics

On quasi-Einstein spacetimes

Shyamal Kumar Hui, Absos Ali Shaikh, and Dae Won Yoon

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The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study quasi-Einstein spacetimes. Some basic geometric properties of such a spacetime are obtained. The applications of quasi-Einstein spacetimes in general relativity and cosmology are investigated. Finally, the existence of such spacetimes are ensured by several interesting examples.

Article information

Tsukuba J. Math., Volume 33, Number 2 (2009), 305-326.

First available in Project Euclid: 26 February 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53B30: Lorentz metrics, indefinite metrics 53B50: Applications to physics 53C50: Lorentz manifolds, manifolds with indefinite metrics 53C80: Applications to physics 83D05: Relativistic gravitational theories other than Einstein's, including asymmetric field theories

quasi-Einstein spacetime cyclic parallel Ricci tensor conformally flat scalar curvature energy-momentum tensor Codazzi tensor perfect fluid spacetime Killing vector field


Shaikh, Absos Ali; Yoon, Dae Won; Hui, Shyamal Kumar. On quasi-Einstein spacetimes. Tsukuba J. Math. 33 (2009), no. 2, 305--326. doi:10.21099/tkbjm/1267209423. https://projecteuclid.org/euclid.tkbjm/1267209423

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