Spatially Homogeneous World Models

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Abstract
We obtain the field equations of Einstein for spatially homogeneous spaces as the Euler‐Lagrange equations of a variational problem. We write these equations in Hamiltonian form and regularize them. In this way, we obtain a class of solutions without rotations. We derive, in particular, the Lagrangian function for the rotating model with the S3 group first computed by Gödel. We suggest that the corresponding Hamiltonian equations can be regularized.