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The General Static Spherically Symmetric Solution of the "Weak" Unified Field Equations

Published online by Cambridge University Press:  20 November 2018

J. R. Vanstone
J. R. Vanstone*
Affiliation:
University of Toronto and Summer Research Institute of the Canadian Mathematical Congress
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In 1947 Einstein and Strauss (2) proposed a unified field theory based on a four-dimensional manifold characterized by a nonsymmetric tensor gij and a non-symmetric connection , where

(1)

Using a variational principle in which gij and are independently varied, the above authors obtain the equivalent of the following field equations:

(2a)

(2b)

In these equations a comma denotes partial differentiation with respect to the co-ordinates of the manifold, Wij is the Ricci tensor formed from and the notation

for the symmetric and skew-symmetric parts of geometric objects Q is employed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 568 - 576
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Bonnor, , Solutions statiques à symétrie sphérique dans la théorie du champ unifié d'Einstein, Proc. Roy. Soc, 209 (1951), 353, and 210 (1952), 427.Google Scholar
2. Einstein, A. and Strauss, E., Ann. Math., 47 (1946), 731.Google Scholar
3. Mavridès, , Solution non statique à symétrie sphérique des équations de la théorie unitaire d'Einstein, C.R. Acad. Sci., 239 (1954), 1597.Google Scholar
4. Papapetrou, , Static spherically symmetric solutions in the unitary field theory, Proc. Roy. Ir. Acad., Sect. A, 52 (1948), 69.Google Scholar
5. Tonnelat, , La théorie du champ unifié d'Einstein, Paris (1955).Google Scholar
6. Wyman, Max, Unified field theory, Can. J. Math., 2 (1950), 427.Google Scholar