Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-10-30
Phys.Rev.D77:043520,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
50 pages, 4 figures
Scientific paper
10.1103/PhysRevD.77.043520
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} $\beta^a, {\cal N}^a{}_i$); (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 $\beta, {\cal{N}}$ whose asymptotic behavior is described by a solution $\beta_{[0]}, {\cal N}_{[0]}$ of the previous evolution system by means of a `\it{generalized Fuchsian system}' for the differenced variables $\bar \beta = \beta - \beta_{[0]}$, $\bar {\cal N} = {\cal N} - {\cal N}_{[0]}$, and by requiring that $\bar \beta$ 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.
Buyl Sophie de
Damour Thibault
No associations
LandOfFree
Describing general cosmological singularities in Iwasawa variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Describing general cosmological singularities in Iwasawa variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Describing general cosmological singularities in Iwasawa variables will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-365788