Describing general cosmological singularities in Iwasawa variables
| dc.creator | Damour, Thibault | |
| dc.creator | de Buyl, Sophie | |
| dc.date | 2007-10-30 | |
| dc.date.accessioned | 2026-07-07T11:12:47Z | |
| dc.date.available | 2026-07-07T11:12:47Z | |
| dc.description | Belinskii, Khalatnikov, and Lifshitz (BKL) conjectured that the description of the asymptotic behavior of a generic solution of Einstein equations near a spacelike singularity could be drastically simplified by considering that the time derivatives of the metric asymptotically dominate (except at a sequence of instants, in the `chaotic case') over the spatial derivatives. We present a precise formulation of the BKL conjecture (in the chaotic case) that consists of basically three elements: (i) we parametrize the spatial metric $g_{ij}$ by means of \it{Iwasawa variables} $β^a, {\cal N}^a{}_i$); (ii) we define, at each spatial point, a (chaotic) \it{asymptotic evolution system} made of ordinary differential equations for the Iwasawa variables; and (iii) we characterize the exact Einstein solutions $β, {\cal{N}}$ whose asymptotic behavior is described by a solution $β_{[0]}, {\cal N}_{[0]}$ of the previous evolution system by means of a `\it{generalized Fuchsian system}' for the differenced variables $\bar β= β- β_{[0]}$, $\bar {\cal N} = {\cal N} - {\cal N}_{[0]}$, and by requiring that $\bar β$ and $\bar {\cal N}$ tend to zero on the singularity. We also show that, in spite of the apparently chaotic infinite succession of `Kasner epochs' near the singularity, there exists a well-defined \it{asymptotic geometrical structure} on the singularity : it is described by a \it{partially framed flag}. Our treatment encompasses Einstein-matter systems (comprising scalar and p-forms), and also shows how the use of Iwasawa variables can simplify the usual (`asymptotically velocity term dominated') description of non-chaotic systems. | |
| dc.description | 50 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0710.5692 | |
| dc.identifier | http://arxiv.org/abs/0710.5692 | |
| dc.identifier | Phys.Rev.D77:043520,2008 | |
| dc.identifier | doi:10.1103/PhysRevD.77.043520 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/191496 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Describing general cosmological singularities in Iwasawa variables | |
| dc.type | text |