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".

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This is a review of recent progress concerning generic spacelike singularities in general relativity. For brevity the main focus is on singularities in vacuum spacetimes, although the connection with, and the role of, matter for generic singularity formation is also commented on. The paper describes recent developments in two areas and show how these are connected within the context of the conformally Hubble-normalized state space approach. The first area is oscillatory singularities in spatially homogeneous cosmology and the connection between asymptotic behaviour and heteroclinic chains. The second area concerns oscillatory singularities in inhomogeneous models, especially spike chains and recurring spikes. The review also outlines some underlying reasons for why the structures that are the foundation for generic oscillatory behaviour exists at all, which entails discussing how underlying physical principles and applications of solution generating techniques yield hierarchical structures and connections between them. Finally, it is pointed out that recent progress concerning generic singularities motivates some speculations that suggest that a paradigm shift concerning their physical role, and what mathematical issues to address, might be in order.
    General Relativity and Gravitation 04/2013; 45(9). DOI:10.1007/s10714-013-1556-3 · 1.73 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The second deals with generic oscillatory singularities in inhomogeneous cosmologies, especially those with two commuting spacelike Killing vectors. This paper describes recent progress in these two areas: in the spatially homogeneous case focus is on mathematically rigorous results, while analytical and numerical results concerning generic behavior and so-called recurring spike formation are the main topic in the inhomogeneous case. Unifying themes are connections between asymptotic behavior, hierarchical structures, and solution generating techniques, which provide hints for a link between the nature of generic singularities and a hierarchy of hidden asymptotic symmetries.
    International Journal of Modern Physics D 06/2013; 22(3). DOI:10.1142/S0218271813300024 · 1.42 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We rigorously verify that in the spatially homogeneous spacetimes (Bianchi VIII and IX), the presence of matter does not affect the oscillatory behavior of the solutions to the Einstein field equations as first conjectured by Belinski, Khalatnikov, and Lifshitz (BKL) in 1970. This paper is an extension of the paper by Reiterer and Trubowitz (arXiv 1005.4908) and uses the same formalism. We use the ultrarelativistic equation of state.

Full-text (2 Sources)

Available from
Aug 6, 2014