Spike Oscillations

Abstract

According to Belinskii, Khalatnikov and Lifshitz (BKL), a generic spacelike singularity is characterized by asymptotic locality: Asymptotically, toward the singularity, each spatial point evolves independently from its neighbors, in an oscillatory manner that is represented by a sequence of Bianchi type I and II vacuum models. Recent investigations support a modified conjecture: The formation of spatial structures (`spikes') breaks asymptotic locality. The complete description of a generic spacelike singularity involves spike oscillations, which are described by sequences of Bianchi type I and certain inhomogeneous vacuum models. In this paper we describe how BKL and spike oscillations arise from concatenations of exact solutions in a Hubble-normalized state space setting, suggesting the existence of hidden symmetries and showing that the results of BKL are part of a greater picture.

38 pages, 14 figures

References in corpus (9)

• Analytic description of singularities in Gowdy spacetimes
• Classical and Quantum Features of the Mixmaster Singularity
• Spikes in the Mixmaster regime of G_2 cosmologies
• Mixmaster: Fact and Belief
• New explicit spike solution -- non-local component of the generalized Mixmaster attractor
• A new proof of the Bianchi type IX attractor theorem
• Generating matter inhomogeneities in general relativity
• Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles
• Statistical Properties of Cosmological Billiards

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• Open problems in mathematical physics
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• Future instability of FLRW fluid solutions for linear equations of state $p=K\rho$ with $1/3<K<1$
• Stiff fluid spike solutions from Bianchi type V seed solutions
• A Scenario for a Singularity-free Generic Cosmological Solution
• Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes
• Non-orthogonally transitive $G_2$ spike solution
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• Transition analysis of the non-OT $G_2$ stiff fluid spike solution
• Numerical confirmations of joint spike transitions in $G_2$ cosmologies
• Semiclassical study of the Mixmaster model: the quantum Kasner map
• Dynamical Equilibrium States of a Class of Irrotational Non-Orthogonally Transitive $G_2$ Cosmologies I: The Conjecture of Chaotic Cosmological Inhomogeneity