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- W2951022425 abstract "The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of Belinskii-Khalatnikov-Lifshitz and technically simplified by the use of the Arnowitt-Deser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solution is describable, at each (generic) spatial point, as a billiard motion in an auxiliary Lorentzian space. For certain Einstein-matter systems, notably for pure Einstein gravity in any spacetime dimension D and for the particular Einstein-matter systems arising in String theory, the billiard tables describing asymptotic cosmological behaviour are found to be identical to the Weyl chambers of some Lorentzian Kac-Moody algebras. In the case of the bosonic sector of supergravity in 11 dimensional spacetime the underlying Lorentzian algebra is that of the hyperbolic Kac-Moody group E_{10}, and there exists some evidence of a correspondence 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}." @default.
- W2951022425 created "2019-06-27" @default.
- W2951022425 creator A5068574814 @default.
- W2951022425 date "2004-12-21" @default.
- W2951022425 modified "2023-09-27" @default.
- W2951022425 title "Cosmological Singularities, Billiards and Lorentzian Kac-Moody Algebras" @default.
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