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.

在这项研究中，我们分析了具有格雷分解的几乎伪 Ricci 对称时空，以及广义的 Robertson-Walker 时空。对于几乎伪 Ricci 对称时空，我们确定了 Ricci 张量梯度的 Gray 分解提供的所有O ( n ) 不变子空间中 Ricci 张量的形式。在三种情况下，我们得到 Ricci 张量是完美流体的形式，在一种情况下，时空变成了广义的 Robertson-Walker 时空。在其他情况下，我们会得到一些代数结果。最后证明了一个近似伪里奇对称的广义罗伯逊-沃克时空是一个完美的流体时空。