Apparaît dans la collection : General relativity: a celebration of the 100th anniversary

Belinskii, Khalatnikov and Lifshitz (BKL) introduced the idea that the geometry of spacetime near a generic, inhomogeneous cosmological (i. e. spacelike) singularity has (for the four-dimensional vacuum Einstein equations) a chaotic structure. After reviewing the status of BKL ideas as well as their extension to the higher-dimensional vacuum Einstein equations, and to the Einstein-matter systems of most relevance in the context of current theoretical physics, we shall present a precise formulation of the BKL conjecture (in the chaotic case) in terms of an Iwasawa-type parametrization of the spatial metric. We shall also present recent developments suggesting that the chaotic BKL behavior is the shadow of a hidden symmetry (possibly related to M-theory dualities) involving infinite-dimensional hyperbolic Kac-Moody algebras. https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-thibaultdamour.pdf