A Topological Temporal Framework for the Unification of Gravity and Electromagnetism

We present a unified geometrical and topological framework for gravity and electromagnetism in which a unit-norm, future-directed timelike vector field Φµ encodes intrinsic temporal directionality. Within this formalism, both gravitational and electromagnetic interactions emerge from a single covariant variational principle rooted in the geometry and phase topology of Φµ . The U(1) gauge symmetry of electromagnetism arises naturally from the local phase θ(x) of the Chronon field, and its associated curvature yields Maxwell dynamics. The Einstein-Maxwell equations are recovered in the weak-field limit, and electric charge quantization follows from topological constraints via the fundamental group π1(U(1)) = Z. This approach offers a minimal, four-dimensional, and testable reformulation of classical unification without invoking extra dimensions or auxiliary gauge sectors.