Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-12-20
Class.Quant.Grav. 20 (2003) R145-R200
Physics
High Energy Physics
High Energy Physics - Theory
88 pages
Scientific paper
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 $D \geq 4$. 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.
Damour Thibault
Henneaux Marc
Nicolai Hermann
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