Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-04-11
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, one diagram; invited talk at the 11th Marcel Grossmann Meeting on Recent Developments in General Relativity, Berlin,
Scientific paper
We review the recently discovered interplay between chaos and symmetry in the general inhomogeneous solution of many string-related Einstein-matter systems in the vicinity of a cosmological singularity. The Belinsky-Khalatnikov-Lifshitz-type chaotic behaviour is found, for many Einstein-matter models (notably those related to the low-energy limit of superstring theory and M-theory), to be connected with certain (infinite-dimensional) hyperbolic Kac-Moody algebras. In particular, the billiard chambers describing the asymptotic cosmological behaviour of pure Einstein gravity in spacetime dimension d+1, or the metric-three-form system of 11-dimensional supergravity, are found to be identical to the Weyl chambers of the Lorentzian Kac-Moody algebras AE_d, or E_{10}, respectively. This suggests that these Kac-Moody algebras are hidden symmetries of the corresponding models. There even exists some evidence of a hidden equivalence between the general solution of the Einstein-three-form system and a null geodesic in the infinite dimensional coset space E_{10} / K(E_{10}), where K(E_{10}) is the maximal compact subgroup of E_{10}.
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