The BKL Conjectures for Spatially Homogeneous Spacetimes

Source: arXiv


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".

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Available from: Michael Reiterer, Aug 06, 2014
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    • "When this extra condition is satisfied it can be shown, using a theorem of Takens, that the flow near any vertex of the chain is equivalent to the linearized flow by a diffeomorphism. Some investigations of the case of chains which may approach the Taub points have been carried out in [15] "
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    ABSTRACT: One way to understand more about spacetime singularities is to construct solutions of the Einstein equations containing singularities with prescribed properties. The heuristic ideas of the BKL picture suggest that oscillatory singularities should be very common and give a detailed picture of how these could look. The more straightforward case of singularities without oscillations is reviewed and existing results on that subject are surveyed. Then recent theorems proving the existence of spatially homogeneous solutions with oscillatory singularities of a specific type are presented. The proofs of these involve applications of some ideas concerning heteroclinic chains and their stability. Some necessary background from the theory of dynamical systems is explained. Finally some directions in which this research might be generalized in the future are pointed out.
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    • "Specifically, the dynamics of each spatial point follow the 'Mixmaster' behavior —a sequence of Bianchi I solutions bridged by Bianchi II transitions. By now there is considerable support for this conjecture both from rigorous mathematical and numerical investigations [12] [13] [14] [15]. This provides some support for the idea that lessons on the quantum nature of the big-bang (and big-crunch) singularities in Bianchi models may be valid much more generally. "
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