Time asymmetry and chaos in general relativity (Q701985)

Bianchi-type-VIII models attracted much attention because they are among the most general homogeneous solutions of Einstein's gravitational field equations and show a chaotic (so-called mixmaster) behavior towards the cosmological singularity. Around 1971, the latter was shown by Belinskii, Khalatnikov and Lifshitz (BKL) who discussed it with the aim to free General Relativity from the suspicion that it allows only for cosmological models that start or end in a singularity. The situation was clarified by the singularity theorems of Penrose and Hawking, the more proper mathematical formulation of the BKL approach by Misner, and a rediscussion of the BKL papers by Barrow and Tipler. Now the author of the present paper dicusses another aspect of the BKL approach. His discussion is motivated by diverging results concerning the late-time behavior of Bianchi-type-VIII models. In contrast to the author, P. Halpern, by using the BKL approach, obtained the result that chaos continues in the far future of these models. Therefore, again a question as to the applicability of the BKL method arises: Can this method which was invented for investigations at early times close to the initial singularity also be used for late-time investigation? The author shows what, in contrast to Halpern's application of this method, has to be changed such that, at a heuristical level, the BKL method gives a valid approximation also of the late-time evolution of the type-VIII models and provides a non-chaotic behavior.