Spatially Homogeneous World Models

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.