Spatially Homogeneous Dynamics: A Unified Picture
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.
Keywords
Cite
@article{arxiv.gr-qc/0102035,
title = {Spatially Homogeneous Dynamics: A Unified Picture},
author = {Robert T. Jantzen},
journal= {arXiv preprint arXiv:gr-qc/0102035},
year = {2007}
}
Comments
84 pages in latex(2e) article style with 10 encapsulated postscript figures, uses graphics package; reformatted with corrections from out-of-print book Proc. Int. Sch. Phys. "E. Fermi" Course LXXXVI (1982) on "Gamov Cosmology" (R. Ruffini, F. Melchiorri, Eds.), North Holland, Amsterdam, 1987, 61-147; resurrected from behind the "literature horizon"