2003/04/15 by Thibault Damour, Marc Henneaux, Hermann Nicolai · 7 citations
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Physics #Dynamical billiards #Hyperboloid #Mathematical physics #Spacetime #Dilaton #Diagonal #Classical mechanics #Singularity #Minkowski space #Theoretical physics #Scale invariance #Tangent space #Quantum mechanics #Pure mathematics #Mathematical analysis #Geometry #Mathematics
paper · pdf · doi:10.1088/0264-9381/20/9/201
openalex publication_date 2003/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 a 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 nonlinear σ-model formally invariant under the corresponding Kac–Moody group.