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Spatially Homogeneous Dynamics: A Unified Picture

Robert T. Jantzen
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Abstract

The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial homogeneity. A parameter-dependent decomposition of the metric variables adapted to the symmetry breaking effects of the nonabelian Bianchi types on the "free dynamics" leads to a reduction of the equations of motion for those variables to a 2-dimensional time-dependent Hamiltonian system containing various time-dependent potentials which are explicitly described and diagrammed. These potentials are extremely useful in deducing the gross features of the evolution of the metric variables.

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Robert T. Jantzen. 2001-02-12. Spatially Homogeneous Dynamics: A Unified Picture. https://arxiv.org/abs/gr-qc/0102035

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