Einstein billiards and spatially homogeneous cosmological models
arXiv:hep-th/0306280 · doi:10.1088/0264-9381/20/23/012
Abstract
In this paper, we analyse the Einstein and Einstein-Maxwell billiards for all spatially homogeneous cosmological models corresponding to 3 and 4 dimensional real unimodular Lie algebras and provide the list of those models which are chaotic in the Belinskii, Khalatnikov and Lifschitz (BKL) limit. Through the billiard picture, we confirm that, in D=5 spacetime dimensions, chaos is present if off-diagonal metric elements are kept: the finite volume billiards can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody algebras. The most generic cases bring in the same algebras as in the inhomogeneous case, but other algebras appear through special initial conditions.
27 pages, 10 figures, additional possibility analysed in section 4.3, references added, typos corrected
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- Exact solutions for Bianchi type cosmological metrics, Weyl orbits of E_{8(8)} subalgebras and p--branes
- Billiard representation for multidimensional multi-scalar cosmological model with exponential potentials
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- Hidden symmetries in mixmaster-type universe