Geometric and Physical Properties of Twisted Sequential Warped Product Manifolds with Applications

This paper introduces twisted sequential warped products. This new class of warped products extends solutions to Einstein’s field equations. We derive explicit formulas for covariant derivatives, curvature tensors, Ricci curvature, and scalar curvature. We characterize Einstein conditions and analyze geodesics. We also study conformal vector fields, including Killing and concircular types. Furthermore, we examine gradient almost Ricci solitons and the concircular curvature tensor. Explicit examples of such manifolds are presented, and applications to cosmology, black hole physics, and quantum field theory are discussed. These findings deepen the understanding of warped product geometry in general relativity. They also provide a foundation for further research.