Summary
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 Møller-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.
Similar content being viewed by others
References
Papapetrou A.,Proc. R. Soc. London, Ser. A,209 (1951) 248.
Tulczyjew W.,Acta Phys. Polon.,18 (1959) 393.
Taub A. H.,J. Math. Phys.,5 (1964) 112.
Pirani F.,Acta Phys. Polon,15 (1956) 389.
Cattaneo C.,Mem. Ann. Mat. Pura Appl., S. IV,48 (1959) 361.
Jantzen R. T., Carini P., andBini D.,Ann. Phys. (N.Y.),215 (1992) 1.
Ferrarese G.,Lezioni di relatività generale (Pitagora Editrice, Bologna) 1994.
Corinaldesi E., andPapapetrou A.,Proc. R. Soc. London, Ser. A,209 (1951) 259.
Dixon W. G.,Proc. R. Soc. London, Ser. A,314 (1970) 499.
Dixon W. G.,Gen. Relativ. Gravit.,4 (1973) 199.
Ehlers J., andRudolph E.,Gen. Relativ. Gravit.,8 (1977) 197.
Madore J.,Ann. Inst. H. Poincaré,11 (1969) 221.
Cantoni V.,Rend. Acc. Lincei,36 (1964) 461.
Tod K. P., De Felice F. andCalvani M.,Nuovo Cimento B,34 (1976) 365.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ferarese, G., Bini, D., Stazi, L. et al. Dynamics of a relativistic spinning particle. Nuov Cim B 111, 217–225 (1996). https://doi.org/10.1007/BF02724646
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02724646