Geometry of semi pseudo-Ricci symmetric spacetimes under Gray’s decomposition

Abstract

In this paper, we characterize semi-pseudo Ricci symmetric spacetimes thriving with Gray‟s decomposition as well as generalized Robertson-Walker spacetimes. For semi pseusdo–Ricci symmetric spacetimes, we determine the form of the Ricci tensor in all ( )-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 spacetimes. Finally, it is shown that a semi-pseudo Ricci symmetric generalized Robertson-Walker spacetime is a perfect spacetime.