Abstract
We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Carmeli,Found. Phys. 15, 175 (1985).
M. Carmeli and S. Malin,Found. Phys. 15, 185 (1985).
M. Carmeli and S. Malin,Found. Phys. 15, 1019 (1985).
M. Carmeli and S. Malin,Found. Phys. 16, 791 (1986).
M. Carmeli and S. Malin,Found. Phys. 17, 193 (1987).
M. Carmeli,Found. Phys. 15, 1263 (1985).
M. Carmeli,Int. J. Theor. Phys. 25, 89 (1986).
L. D. Landau and E. M. Lifshitz,The Classical Theory of Fields (Pergamon Press, London, 1975).
C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (W. H. Freeman, San Francisco, 1973).
S. Weinberg,Gravitation and Cosmology (Wiley, New York, 1972).
S. W. Hawking and G. F. R. Ellis,The Large-Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973).
A. Einstein and J. Grommer,Sitzungsber. Preuss. Acad. Wiss., Phys. Math. Kl, 2 (1927).
A. Einstein, L. Infeld, and B. Hoffmann,Ann. Math. 39, 65 (1938).
A. Einstein and L. Infeld,Can. J. Math. 1, 209 (1949).
V. Fock,Rev. Mod. Phys. 29, 325 (1957).
V. Fock,The Theory of Sapce, Time, and Gravitation (Pergamon, London, 1959).
M. Carmeli,Nuovo Cimento Lett. 36, 428 (1983).
L. P. Eisenhart,Riemannian Geometry (Princeton University Press, Princeton, New Jersey, 1949).
D. J. Struik,Lectures on Classical Differential Geometry (Addison-Wesley, Reading, Massachusetts, 1950).
H. Goldstein,Classical Mechanics (Addison-Wesley, Reading, Massachusetts, 1950).
Author information
Authors and Affiliations
Additional information
On leave from the Center for Theoretical Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.
Rights and permissions
About this article
Cite this article
Carmeli, M., Malin, S. Field theory onR×S 3 topology. VI: Gravitation. Found Phys 17, 407–417 (1987). https://doi.org/10.1007/BF00733377
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00733377