Vanishing Pseudo W8-Curvature and Its Implications for Spacetime Relativity

This paper provides an analysis of spacetimes characterized by the pseudo W8curvature tensor, with particular focus on their geometric and physical properties within the framework of Einstein’s field equations. The study investigates pseudo W8-flat spacetimes as potential Einstein manifolds and examines the associated covariant properties of the energy-momentum tensor, including scenarios with a cosmological constant. It also explores perfect fluid models with vanishing pseudo W8-curvature to understand the behavior of energy density and isotropic pressure, particularly under the timelike convergence condition and its relation to the strong energy condition. Dust-type fluid spacetimes are considered to analyze vacuum solutions with non-zero energy density and their geometric structure. Additionally, the paper constructs explicit spacetime models to illustrate the geometric and physical implications of the vanishing pseudo W8-curvature condition.