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Generalized Ricci recurrent spacetimes (GR) n are investigated in Gray's seven subspaces. It is proved that a (GR) n spacetime in all subspaces but one is an Einstein spacetime. The subspace ℐ cannot contain a (GR) n spacetime. Further, the subspaces ℐ ⊕ A and ℐ ⊕ B reduce to A and B , respectively. Next, we prove that a (GR) n spacetime is Ricci semi-symmetric if and only if either the spacetime is Einstein or the vector field Al is closed. Further, it is shown that the Ricci tensor of (GR) n is Riemann compatible if Al is closed. Finally, sufficient conditions are given on a (GR) n warped product manifold to guarantee that the factor manifolds are Einstein. Moreover, it is shown that a generalized Ricci recurrent GRW spacetime is an Einstein spacetime. [ABSTRACT FROM AUTHOR]

In this study, we analyze almost pseudo-Ricci symmetric spacetimes endowed with Gray's decomposition, as well as generalized Robertson—Walker spacetimes. For almost pseudo-Ricci symmetric spacetimes, we determine the form of the Ricci tensor in all the O (n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. In three cases we obtain that the Ricci tensor is in the form of perfect fluid and in one case the spacetime becomes a generalized Robertson—Walker spacetime. In other cases we obtain some algebraic results. Finally, it is shown that an almost pseudo-Ricci symmetric generalized Robertson—Walker spacetime is a perfect fluid spacetime. [ABSTRACT FROM AUTHOR]