Einstein-like Poisson Warped Product Manifolds and Applications

In this paper, we introduce the concept of contravariant Einstein-like Poisson manifolds of classes $\mathcal{A}$, $\mathcal{B}$, and $\mathcal{P}$. We then prove that the fiber space of a Poisson warped product manifold inherits the contravariant Einstein-like classes of the total space, while the base space inherits these classes under certain conditions related to the warping function. We also explore applications of contravariant Einstein-like Poisson structures in various spacetime models, including generalized Robertson–Walker, Reissner–Nordström, and standard static spacetimes.