Higgs field and Gravitational field

Could the Higgs field (HF) be equated with the gravitational field (GF)? This seems plausible since the Einstein Field Equations (EFE) Describe the curvature of space time an object with mass (given by The Higgs Boson) causes. Mass tells space how to curve, and the curvature tells mass how to move. If they can be equated (HF:=:GF), then the HF could be put in the form of f(x,y,z,t) and solved as EFE, a nonlinear system of partial differential equations, hard but possibly doable.