Abstract
The validity of imposing spatial homogeneity on the variations in the usual action principle for Einstein's equations is studied. It is proved that with this procedure the standard and ADM Lagrangians give correct Einstein equations if and only if the space belongs to Class A of Ellis and MacCallum [1], i.e., the structure constants of the simply transitive group satisfy C f fg =0. The possibility of overcoming this difficulty in the Class B spaces is examined.
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This work was supported in part by the United States Atomic Energy Commission under Contract Number AT 104-37-39 Project Agreement No. 125.
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MacCallum, M.A.H., Taub, A.H. Variational principles and spatially-homogeneous universes, including rotation. Commun.Math. Phys. 25, 173–189 (1972). https://doi.org/10.1007/BF01877589
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DOI: https://doi.org/10.1007/BF01877589