Hyperbolic KacMoody algebras and chaos in KaluzaKlein models
Abstract
Some time ago, it was found that the neverending oscillatory chaotic behaviour discovered by Belinskii, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike (``cosmological'') singularity disappears in spacetime dimensions /D≡d+1>10. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic KacMoody algebra. In this Letter we show that the same connection applies to pure gravity in any spacetime dimension />=4, where the relevant algebras are AE_{d}. In this way the disappearance of chaos in pure gravity models in /D>=11 dimensions becomes linked to the fact that the KacMoody algebras AE_{d} are no longer hyperbolic for /d>=10.
 Publication:

Physics Letters B
 Pub Date:
 June 2001
 DOI:
 10.1016/S03702693(01)004981
 arXiv:
 arXiv:hepth/0103094
 Bibcode:
 2001PhLB..509..323D
 Keywords:

 High Energy Physics  Theory;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages, 1 figure