Novel Theorems on Spacetime Admitting Pseudo‐W ₂ Curvature Tensor

This paper investigates spacetime manifolds admitting a pseudo‐ W 2 curvature tensor. We show that a pseudo‐ W 2 flat spacetime is an Einstein manifold and therefore has constant curvature. Moreover, when the manifold satisfies the Einstein field equations (EFE), with a cosmological constant, the associated energy–momentum tensor is covariantly constant. We further determine the length of the Ricci operator in a pseudo‐ W 2 flat perfect fluid spacetime and prove that, under the EFE without a cosmological constant, such a spacetime possesses constant energy density and isotropic pressure. Finally, an explicit example of a spacetime admitting a pseudo‐W2 curvature tensor is constructed to validate the results using differential equations.