2003/04/01 by Claes Uggla, Henk van Elst, John Wainwright +3 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #astro-ph #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.68.103502
published as Phys.Rev. D68 (2003) 103502 · 31 pages, 10 *.ps figures, 3 tables, LaTeX2e (10pt), submitted for publication to Physical Review D
arxiv created 2003/04/01 · openalex publication_date 2003/11/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of Einstein's field equations with a perfect fluid matter source as an autonomous system of evolution equations and constraints. This framework incorporates spatially homogeneous dynamics in a natural way as a special case, thereby placing earlier work on spatially homogeneous cosmology in a broader context, and allows us to draw on experience gained in that field using dynamical systems methods. One of our goals is to provide a precise formulation of the approach to the spacelike initial singularity in cosmological models, described heuristically by Belinski\ifmmode \checki\else \vi\fi, Khalatnikov and Lifshitz. Specifically, we construct an invariant set which we conjecture forms the local past attractor for the evolution equations. We anticipate that this new formulation will provide the basis for proving rigorous theorems concerning the asymptotic behavior of spatially inhomogeneous cosmological models.