Erweiterte Gravitationstheorie, Machsches Prinzip und rotierende Massen

Abstract

The rotation of the local inertial frames induced by a rotating shell of mass is calculated in the framework of P. Jordan’s “extended theory of gravitation”. As a special case, the corresponding results are obtained for Brans and Dicke’s “scalar-tensor” theory. In the weak field approximation the result is the same as the Lense-Thirring effect of General Relativity, except for a factor depending on the coupling constant of the scalar field. The strong field limit in which the inertial frame is completely dragged along by the rotating shell is investigated. In particular it is shown that this limit of perfect dragging occurs in certain cosmological models whenever the density of the rest of the matter in the universe tends to zero. This result is interpreted as a manifestation of Mach’s principle in the extended theory of gravitation.