2002/12/20 by T. Damour, M. Henneaux, H. Nicolai · 1 citation
Physics and Astronomy · #hep-th #astro-ph #gr-qc
published as Class.Quant.Grav.20:R145-R200,2003 · 88 pages
arxiv created 2002/12/20 · arxiv updated 2014/11/17
It is shown in detail that the dynamics of the Einstein-dilaton-p-form system in the vicinity of a spacelike singularity can be asymptotically described, at a generic spatial point, as a billiard motion in a region of Lobachevskii space (realized as an hyperboloid in the space of logarithmic scale factors). This is done within the Hamiltonian formalism, and for an arbitrary number of spacetime dimensions D ≥ 4. A key role in the derivation is played by the Iwasawa decomposition of the spatial metric, and by the fact that the off-diagonal degrees of freedom, as well as the p-form degrees of freedom, get ``asymptotically frozen'' in this description. For those models admitting a Kac-Moody theoretic interpretation of the billiard dynamics we outline how to set up an asymptotically equivalent description in terms of a one-dimensional non-linear sigma-model formally invariant under the corresponding Kac-Moody group.