Characterizations of mixed quasi-Einstein spacetimes under Gray’s decomposition

Abstract

In this study, we analyze mixed quasi-Einstein spacetimes endowed with Gray’s decomposition, as well as generalized Robertson–Walker spacetimes. For mixed quasi-Einstein spacetimes, the shape of the Ricci tensor in all [Formula: see text]-invariant subspaces can be identified using Gray’s decomposition of the gradient of the Ricci tensor. In case one, such a spacetime is found to be static; in three cases, the Ricci tensor is found to be in the form of a  perfect fluid; and in the other three situations, the spacetime becomes a quasi-Einstein spacetime under certain restrictions on the associated vector fields. Finally, it is established that a mixed quasi-Einstein generalized  Robertson–Walker spacetime is a perfect fluid spacetime.