The Mixmaster Cosmological Metrics
This paper begins with a short presentation of the Bianchi IX or “Mixmaster” cosmological model, and some ways of writing the Einstein equations for it. There is then an interlude describing how I came to a study of this model, and then a report of some mostly unpublished work from a Ph. D. thesis of D. M. (Prakash) Chitre relating approximate solutions to geodesic flows on finite volume negative curvature Riemannian manifolds, for which he could quote results on ergodicity. A final section restates studies of a zero measure set of solutions which in first approximation appear to have only a finite number of Kasner epochs before reaching the singularity. One finds no plausible case for such behavior in better approximations.
KeywordsTangent Direction Fundamental Domain Bianchi Type Potential Term Fuchsian Group
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- Chitre, D. M., 1972a, Investigation of Vanishing of a Horizon for Bianchi Type IX (the Mixmaster) Universe (College Park: University of Maryland Ph. D. thesis).Google Scholar
- Hobill, D., 1994, A brief review of “Deterministic chaos in general relativity”, in this volume.Google Scholar
- —, 1972, Minisuperspace, in Magic Without Magic—J. A. Wheeler 60th Anniversary Volume, J. Klauder, ed., (San Francisco: W. H. Freeman and Co.), pp 441–473.Google Scholar
- Misner, C. W. and A. H. Taub, 1968, A singularity-free empty universe, Zh. Eksp. Teor. Fiz. 55, 233–255, Soviet Physics—JETP 28, 122-133 (1969).Google Scholar
- Rugh, S.E., 1990, Chaotic Behavior and Oscillating Three-volumes in a Space-Time Metric in General Relativity, Cand. Scient. Thesis, The Niels Bohr Institute, Copenhagen.Google Scholar