Einstein billiards and spatially homogeneous cosmological models

Details Einstein billiards and spatially homogeneous cosmological models Einstein billiards and spatially homogeneous cosmological models

2003-06-27

arxiv.org/abs/hep-th/0306280v2

Class.Quant.Grav. 20 (2003) 5141-5160

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 10 figures, additional possibility analysed in section 4.3, references added, typos corrected

Scientific paper

10.1088/0264-9381/20/23/012

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.

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