The BKL Conjectures for Spatially Homogeneous Spacetimes

Source: arXiv

ABSTRACT We rigorously construct and control a generic class of spatially homogeneous (Bianchi VIII and Bianchi IX) vacuum spacetimes that exhibit the oscillatory BKL phenomenology. We investigate the causal structure of these spacetimes and show that there is a "particle horizon". Comment: 49 pages; Section 7 (Causal structure and particle horizons) added, small changes in other sections to support Section 7

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    ABSTRACT: We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation. Comment: Some updates. A shortened version, to appear in the Bulletin of the AMS, is available online at
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    ABSTRACT: We consider cosmological models of Bianchi type. In particular, we are interested in the α-limit dynamics near the Kasner circle of equilibria for Bianchi classes VIII and IX. They correspond to cosmological models close to the big-bang singularity. We prove the existence of a codimension-one family of solutions that limit, for t → −∞, onto a heteroclinic 3-cycle to the Kasner circle of equilibria. The theory extends to arbitrary heteroclinic chains that are uniformly bounded away from the three critical Taub points on the Kasner circle, in particular to all closed heteroclinic cycles of the Kasner map.
    Communications in Mathematical Physics 01/2011; 305(1):59-83. · 1.97 Impact Factor

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Aug 6, 2014