Abstract
This paper shows that general relativity and ordinary continuum models of matter imply the presence of Cartan torsion. The key concept is that torsion can be viewed as translational holonomy per unit area, in the limit of very small areas. Translational holonomy is introduced as the nonclosure of the “development” of a space-time loop into a flat space-time. The translational holonomy around a charged rotating black hole is calculated. If a large collection of small rotating objects is approximated by continuous spinning matter, the resulting torsion and spin have the same relation as in Einstein-Cartan theory, except that the torsion traces remain zero for the simple model of spinning matter used here. Finally, this construction adds torsion to the list of nonpropagating fields which can be viewed as continuum density of holonomy around localized space-time boundaries, or around throats which are connected to further local topological structures.
Similar content being viewed by others
References
Bishop, R. L., and Crittenden, R. J. (1964).The Geometry of Manifolds (Academic Press, New York).
Kobayashi, S., and Nomizu, K. (1963 and 1969).Foundations of Differential Geometry, Vols. I and II (John Wiley and Sons, New York).
Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation (W. H. Freeman Co., San Francisco).
Hehl, F., von der Heyde, P., Kerlick, G. D., and Nester, J. M. (1976).Rev. Mod. Phys.,48(3), 393–416.
Petti, R. (1976).Gen. Rel. Grau,7, 869.
Lorenz, D. (1981).Acta Phys. Polonica,B12(10), 939–950.
Wheeler, J. A. (1962).Geometrodynamics (Academic Press, New York).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Petti, R.J. On the local geometry of rotating matter. Gen Relat Gravit 18, 441–460 (1986). https://doi.org/10.1007/BF00770462
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00770462