The components of a ``vierbein'' system are introduced as field variables in place of the metric tensor in a Riemannian space. The Riemann tensor, which is then written in terms of these new variables, is used to reformulate the Einstein and Einstein‐Maxwell equations with or without a cosmological constant. These field equations have as solutions metrics with Riemann tensor of predetermined algebraic properties.
REFERENCES
1.
2.
Eisenhart, Riemannian Geometry (Princeton University Press Princeton, New Jersey, 1960), Chap. III.
3.
E. Schrödinger, Space‐Time Structure (Cambridge University Press, New York, 1950), Chap. VI.
4.
This identity was pointed out to us by R. Kerr.
5.
6.
7.
J. F. Schell, “A classification of four‐dimensional Riemannian spaces” (preprint).
8.
J. L. Synge, Relativity, the Special Theory (North‐Holland Publishing Company, Amsterdam, 1959), Chap. IX.
9.
Reference 2, Chap. II.
10.
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© 1961 American Institute of Physics.
1961
American Institute of Physics
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