A short note on generalized Robertson Walker spacetimes

In this article, generalized Robertson Walker spacetimes are investigated in light of perfect fluid spacetimes. First, we establish that a perfect fluid spacetime with nonvanishing vorticity whose associated scalars are constant along the velocity vector field becomes a generalized Robertson Walker spacetime. Among others, it is also shown that a Ricci parallel perfect fluid spacetime is either a generalized Robertson Walker spacetime or a static spacetime. Finally, we acquire that in a conformally semisymmetric generalized Robertson Walker spacetime of dimension 4, the scalar curvature vanishes and the spacetime is locally isometric to the Minkowski spacetime, provided the electric part of the Weyl tensor vanishes. Moreover, it is established that the last result also holds in a conformally recurrent generalized Robertson Walker spacetime.