Geometry of Ricci–Bourguignon Solitons on Mixed Doubly Sequential Warped Products: Existence, Classification, and Cosmological Implications

We investigate Ricci–Bourguignon solitons on mixed doubly sequential warped product manifolds. Necessary and sufficient conditions for the existence of such solitons are established, and their implications for Einstein manifolds are analyzed. This work extends previous results on warped product manifolds to the more complex case of mixed doubly sequential warped products. We derive explicit formulas for Ricci tensor components, establish conditions for Einstein metrics, and study gradient solitons and conformal vector fields. Our classification theorems reveal fundamental separability constraints on the warping functions. Applications to cosmological models and black hole solutions demonstrate the physical relevance of these results.