The aim of this paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson–Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson–Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with constant scalar curvature satisfying Einstein’s field equations without cosmological constant is vacuum. Finally, we construct a nontrivial example of pseudosymmetric spacetime.

中文翻译：

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伪对称时空成为完美流体时空的充分条件

本文的目的是获得伪对称时空成为完美流体时空的条件。证明了伪对称广义罗伯逊-沃克时空是完美的流体时空。此外，我们确定共形平坦的伪对称时空是广义的 Robertson-Walker 时空。接下来，证明了具有恒定标量曲率的伪对称尘埃流体满足爱因斯坦场方程而没有宇宙学常数是真空的。最后，我们构建了一个伪对称时空的重要例子。