Dynamics of a relativistic spinning particle

Abstract

We introduce anew intrinsic formulation of Papapetrou’s dynamic equations of a spinning test particle in general relativity, expressed by a first-order linear differential system for a triad of vectors, describing the inner structure of the particle. Within this general scheme we discuss Pirani’s and Moller-Tulczyjew’s supplementary conditions. In both cases these conditions are inadequate for a fully determined dynamic scheme. Indeed, the first gives a second-order differential system for the velocity, and the equation of motion is not normal; the second gives a first-order system which is not determined, because oftwo degrees of indetermination. This result is not in contradiction with the Dixon-Ehlers exact theory of extended bodies, of which the Papapetrou model is an approximation.