Spherically Symmetric and Static Fields in Linearized Gauge Theories of Gravitation

Abstract

In this paper Newtonian limit in the Poincare gauge field theory of gravitation is investigated. In spherically symmetric and static cases interior and exterior solutions of the linearized field equations with gravitational source are obtained by maens of Green's function for the five Lagrangians without ghosts and tachyons. In cases of four Lagrangians, the space-time metrics outside gravitational source are the usual Schwarzschild one of the first-order, while in the case of the fifth Lagrangian the space-time metric differs from the Schwarzschild one. Under both, Newtonian and weak gravitational field approximations, the motion of a test particle without spin should therefore be different from Newton's second law. As a result of the exchanged particles of spin the deviation from Newton's second law is a Yukawa term which is attractive. A distance-dependent gravitational “constant” G(r) can be defined according to the new result. The difference between G(r) and Newton's gravitational constant is due to a nonzero component of torsion tensor, the effect of which can be tested by measuring G(r).