On billiard approach in multidimensional cosmological models
arXiv:0811.2786 · doi:10.1134/S0202289309010137
Abstract
A short overview of the billiard approach for cosmological-type models with n Einstein factor-spaces is presented. We start with the billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin. Then we consider cosmological model with multicomponent "perfect-fluid" and cosmological-type model with composite branes. The second one describes cosmological and spherically-symmetric configurations in a theory with scalar fields and fields of forms. The conditions for appearance of asymptotical Kasner-like and oscillating behaviors in the limit τ\to +0 and τ\to + \infty (where τis a "synchronous-type" variable) are formulated (e.g. in terms of inequalities on Kasner parameters). Examples of billiards related to the hyperbolic Kac-Moody algebras E_{10}, AE_3 and A_{1,II} are given.
18 pages, Latex, based on plenary report at RUSGRAV-13 (23-28 June, 2008, PFUR, Moscow)
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- On Brane Solutions Related to Non-Singular Kac-Moody Algebras
- Black brane solutions related to non-singular Kac-Moody algebras
- Quantum billiards with branes on product of Einstein spaces
- On the "scattering law" for Kasner parameters in the model with one-component anisotropic fluid