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April 2009 The cosmological billiard attractor
J. Mark Heinzle, Claes Uggla, Niklas Röhr
Adv. Theor. Math. Phys. 13(2): 293-407 (April 2009).

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.

Citation

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J. Mark Heinzle. Claes Uggla. Niklas Röhr. "The cosmological billiard attractor." Adv. Theor. Math. Phys. 13 (2) 293 - 407, April 2009.

Information

Published: April 2009
First available in Project Euclid: 17 February 2009

zbMATH: 1170.83003
MathSciNet: MR2481269

Rights: Copyright © 2009 International Press of Boston

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Vol.13 • No. 2 • April 2009
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