Derivation of Einstein's General Relativity Field Equations from Dynamic Vacuum Field Theory

Dynamic Vacuum Field Theory (DVFT) posits that spacetime curvature emerges from distortions in a dynamic vacuum field modeled as a complex scalar ϕ(x)=ρ(x)e^(iθ(x)), where ρ(x) is the vacuum amplitude and θ(x) is the vacuum phase. This paper derives Einstein's field equations of General Relativity (GR) as an effective low-gradient, high-acceleration limit within DVFT. Starting from the fundamental DVFT action, which incorporates the vacuum Lagrangian alongside the Hilbert-Einstein term, we perform variational derivations to obtain the coupled field equations for the metric and vacuum field. In the regime where vacuum perturbations are small and nonlinear effects negligible, the vacuum stress-energy tensor mimics the geometric curvature of GR. This approach offers a physical mechanism for curvature propagation at the speed of light, bridging quantum mechanics with classical relativity. The thesis concludes with implications for unification and references to foundational works.