Characterizations of pseudo quasi-Einstein spacetimes in Gray's decomposition

Abstract

In this study, we analyze pseudo quasi-Einstein spacetimes endowed with Gray's decomposition, as well as generalized Robertson-Walker spacetimes. For pseudo quasi-Einstein spacetimes, we study the form of the Ricci tensor in all the $\mathcal{O}\left(n\right)$-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. In all cases we obtain that the integral curves of the velocity vector field are geodesic under certain restrictions except one case. Also it is established that a pseudo quasi-Einstein generalized Robertson-Walker spacetime is a perfect fluid spacetime. Finally pseudo quasi-Einstein perfect fluid spacetimes have been investigated.