Advances in Theoretical and Mathematical Physics

The cosmological billiard attractor

J. Mark Heinzle, Claes Uggla, and Niklas Röhr

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Abstract

solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike singularities, we derive in a step-by-step manner the cosmological billiard conjecture: we show that the generic asymptotic dynamics of solutions is represented by (randomized) sequences of heteroclinic orbits on the “billiard attractor”. Our analysis rests on two pillars: (i) a dynamical systems formulation based on the conformal Hubblenormalized orthonormal frame approach expressed in an Iwasawa frame; (ii) stochastic methods and the interplay between genericity and stochasticity. Our work generalizes and improves the level of rigor of previous work by Belinskii, Khalatnikov, and Lifshitz; furthermore, we establish that our approach and the Hamiltonian approach to “cosmological billiards”, as elaborated by Damour, Hennaux, and Nicolai, can be viewed as yielding “dual” representations of the asymptotic dynamics.

Article information

Source
Adv. Theor. Math. Phys., Volume 13, Number 2 (2009), 293-407.

Dates
First available in Project Euclid: 17 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1234881637

Mathematical Reviews number (MathSciNet)
MR2481269

Zentralblatt MATH identifier
1170.83003

Citation

Heinzle, J. Mark; Uggla, Claes; Röhr, Niklas. The cosmological billiard attractor. Adv. Theor. Math. Phys. 13 (2009), no. 2, 293--407. https://projecteuclid.org/euclid.atmp/1234881637


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