Contravariant Einstein-like Doubly Warped Metrics: Theory and Applications

In this paper, we extend the study of contravariant Einstein-like metrics to Poisson doubly warped product manifolds (PDWPMs). We derive the necessary and sufficient conditions under which the base and fiber manifolds of a PDWPM inherit Einstein-like structures from the total space. As applications, we construct Einstein-like Poisson doubly warped product structures belonging to classes A, B, and P in various spacetime models, including generalizations of Reissner–Nordström, standard static, and Robertson–Walker spacetimes.