Abstract
We consider metrics which possess a priori certain ‘‘intrinsic symmetries’’ on the three-spaces t=const. In the vacuum case, we obtain a generalization of Birkhoff’s theorem and a set of solutions with a translational isometry operating on the whole space-time. In the nonvacuum case, we assume a perfect fluid matter content and a fluid flow orthogonal to the three-spaces t=const, and obtain several exact analytical solutions, some of them satisfying the standard energy conditions. In particular, a stiff equation of state is obtained in some cases, and we also have found particular solutions where a plane, spherical, or hyperbolic intrinsic symmetry is manifest.
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