Slant curves in Lorentzian twisted warped products: Geometric classification and applications in relativity and cosmology

This paper presents a geometric classification of slant curves in three-dimensional Lorentzian twisted warped product manifolds and establishes their direct relevance to fundamental phenomena in general relativity and cosmology. By characterizing these curves according to their causal structure, timelike, null, and spacelike, we derive explicit formulas for curvature and torsion that correspond to physical observables such as frame-dragging effects, light propagation in anisotropic backgrounds, and cosmic microwave background anomalies. The twisted warped product structure naturally encodes both geometric invariants and their physical counterparts, providing a powerful framework for modeling anisotropic spacetimes, rotating systems, and early-universe cosmology. Our results offer new insights into relativistic particle dynamics, gravitational wave propagation, and precision tests of gravity, with potential applications in satellite-based experiments and theoretical cosmology.