A Saturation Limited Vector Tensor Theory of Gravitation

We present a covariant saturation-limited vector-tensor theory of gravitation in which spacetime dynamics arise from the coupled evolution of a metric tensor and a constrained timelike vector field. A universal saturation constraint enforced by a Lagrange multiplier bounds the vector magnitude. The resulting field equations recover the exact Schwarzschild exterior solution and admit regular interior solutions with finite curvature invariants. The theory reduces exactly to General Relativity in vacuum and weak-field regimes while introducing nonlinear saturation effects that dynamically prevent singularity formation.