Describing general cosmological singularities in Iwasawa variables

Thibault Damour, Sophie de Buyl

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


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 gij by means of Iwasawa variables (βa,Nai); (ii) we define, at each spatial point, a (chaotic) asymptotic evolution system made of ordinary differential equations for the Iwasawa variables; and (iii) we characterize the exact Einstein solutions β, N whose asymptotic behavior is described by a solution β[0], N[0] of the previous evolution system by means of a "generalized Fuchsian system" for the differenced variables β̄=β-β[0], N̄=N-N[0], and by requiring that β̄ and N̄ 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 asymptotic geometrical structure on the singularity: it is described by a 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 nonchaotic systems.

Original languageEnglish
Article number043520
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number4
Publication statusPublished - 20 Feb 2008


Dive into the research topics of 'Describing general cosmological singularities in Iwasawa variables'. Together they form a unique fingerprint.

Cite this