Sophie de Buyl et al 2003 Class. Quantum Grav. 20 5141 doi:10.1088/0264-9381/20/23/012
Sophie de Buyl1, Gaïa Pinardi and Christiane Schomblond
Show affiliationsIn this paper, we analyse the Einstein and Einstein–Maxwell billiards for all spatially homogeneous cosmological models corresponding to three- and four-dimensional real unimodular Lie algebras and provide a 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.
04.20.Gz Spacetime topology, causal structure, spinor structure
17B67 Kac-Moody (super)algebras (structure and representation theory)
Issue 23 (7 December 2003)
Received 27 June 2003
Published 23 October 2003
Sophie de Buyl et al 2003 Class. Quantum Grav. 20 5141
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