Gravity from Poincare Gauge Theory of the Fundamental Particles. III: Weak Field Approximation

Abstract

We apply the weak field approximation to the most general gravitational field equations in Poincaré gauge theory. The weak gravitational field hµν is a multimass field obeying a fourth-order field equation. In the Newtonian approximation we show that there are two routes to arrive at the Newtonian potential. The torsion field is decomposed into six irreducibe building blocks with spinparity, 2+, 2-, 1+, 1-, 0+ and 0-, each of which obeys the Klein-Gordon equation. Finally, we construct a possible candidate for the massless graviton field which obeys the linearized Einstein equation.