Geometric and Physical Characteristics of Pseudo-Schouten Symmetric Manifolds

In this paper, we introduce and conduct a comprehensive study of pseudo-Schouten symmetric manifolds (PSS)n. We establish necessary and sufficient conditions for such a manifold to be Einstein and quasi-Einstein, respectively. Next, we examine pseudo-Schouten symmetric spacetimes within the framework of general relativity. Furthermore, we investigate their role in relativistic spacetime models by considering Einstein’s field equations with and without a cosmological constant. We also show that pseudo-Schouten symmetric spacetimes satisfying Einstein’s equations with a quadratic Killing energy–momentum tensor or a Codazzi-type energy–momentum tensor cannot have non-zero constant scalar curvature. Finally, the existence of pseudo-Schouten symmetric spacetime is shown by constructing an explicit non-trivial example.