Modeling in chaotic relativity

Żardecki, A.

doi:10.1103/physrevd.28.1235

Cited by 39 publications

(17 citation statements)

References 32 publications

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“…Apparent contradictions were found among the results of these numerical experiments themselves, on the one hand, and between these and the results obtained from the analytic analysis of the Gauss map, on the other. For example, numerical experiments by Francisco and Matsas [4] were at odds with earlier numerical results [8] which confirmed the existence of chaos in the system. Francisco and Matsas attributed their observed lack of chaos to the choice of time variable used in the simulations.…”

Section: Introductionmentioning

confidence: 88%

Invariant Lyapunov exponents and chaos in cosmology

Burd¹,

Tavakol

1993

Phys. Rev. D

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The precise dynamical nature of the Bianchi type-IX cosmological model has been a subject of debate for a number of years. The lack of congruence between various results, which mainly employ numerical calculations of the spectrum of Lyapunov exponents, has motivated a number of attempts at a gaugeinvariant characterization of chaos. Here we critically examine one of these attempts and argue that none of the attempted characterizations so far put forward are completely satisfactory. We also briefly discuss natural gauges in cosmology and distinguish between qualitative and quantitative measures of chaos.PACS number(s1: 98.80.H~

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Section: Introductionmentioning

confidence: 88%

Invariant Lyapunov exponents and chaos in cosmology

Burd¹,

Tavakol

1993

Phys. Rev. D

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“…Nevertheless, exponential divergence of initially nearby trajectories was found by other numerical studies yielding positive Lyapunov numbers. This issue was understood when in [64] and [198] numerically and analytically was shown how such calculations depend on the choice of the time variable and parallely to the failure of the conservation of the Hamiltonian constraint in the numerical simulations by [514], although was still debated by [258].…”

Section: Chaos Covariancementioning

confidence: 99%

Classical and Quantum Features of the Mixmaster Singularity

Montani

Battisti

Benini

et al. 2008

Int. J. Mod. Phys. A

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This review article is devoted to analyze the main properties characterizing the cosmological singularity associated to the homogeneous and inhomogeneous Mixmaster model. After the introduction of the main tools required to treat the cosmological issue, we review in details the main results got along the last forty years on the Mixmaster topic. We firstly assess the classical picture of the homogeneous chaotic cosmologies and, after a presentation of the canonical method for the quantization, we develop the quantum Mixmaster behavior. Finally, we extend both the classical and quantum features to the fully inhomogeneous case. Our survey analyzes the fundamental framework of the Mixmaster picture and completes it by accounting for recent and peculiar outstanding results.are obtained requiring the action for the matter S m introduced in Eq. (2.1.11) to be invariant under diffeomorphisms. For the Einstein equations, the Bianchi identities ∇ i G ij = 0 may be viewed as a consequence of the invariance of the Hilbert action under diffeomorphisms. Let us now list the principal aspects of the three fields under consideration.• The energy-momentum tensor of a perfect fluid is given bywhere u i is a unit time-like vector field representing the four-velocity of the fluid. The scalar functions p and ρ are the energy density and the pressure, respectively, as2.8b) where j k is the current density four-vector of electric charge and [ ] denote the antisymmetric sum, or in the forms language equations (2.2.8) are written as d ⋆ F = 4π ⋆ j (2.2.9a) dF = 0 (2.2.9b)where d is the exterior derivative and ⋆ is the Hodge star operator [505,370].

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“…The well-known fact that some very simple dynamic systems with a minimal number of degrees of freedom, no stochastic force and regular initial data may show unpredictable or random behaviour has led to the search for the chaotic conduct of homogeneous cosmological models in the context of general relativity (Barrow, 1981(Barrow, , 1982Chernoff  Barrow, 1983;Cornish  Levin, 1997;Latifi, Musette,  Conte, 1994;Lin  Wald, 1990;Zardecki, 1983). Currently, the so called Mixmaster universe model-a particular Bianchi type universe (Barrow, 1981(Barrow, , 1982Chernoff  Barrow, 1983;Latifi, Musette,  Conte, 1994;Lin  Wald, 1990;Misner, 1969)-has brought into existence a great number of papers in the literature asserting its chaotic conduct (Barrow, 1981(Barrow, , 1982Chernoff  Barrow, 1983;Cornish  Levin, 1997;Latifi, Musette,  Conte, 1994;Lin  Wald, 1990;Misner, 1969;Zardecki, 1983). Accordingly, the verdict has been that this deterministic model is unpredictable with respect to the number of Kasner epochs that comprise each major cycle of its time evolution (Balinskii  Khalatnikov, 1970a;Misner, 1969).…”

Section: Introductionmentioning

confidence: 99%

BKL Method in the Bianchi IX Universe Model Revisited

Lugo¹,

Chauvet²

2013

APR

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Given the extreme difficulty in finding analytical solutions to Einstein’s equations for universe models, such as the Bianchi type IX, different physical-mathematical techniques have been designed to attempt to find, at least approximate solutions that could have relevance in modern cosmology. Belinskii, Khalatnikov and Lifshitz (BKL) have developed a method to study a particular time evolution dynamic of the Bianchi type IX universe model. Herein, it is shown that this method contains pitfalls. These pitfalls, among other things, prevent the conclusion that this model provides chaotic behaviour. We show that the initial presumption made by BKL turns out to be inconsistent with the assumed initial conditions, since it cannot be kept along with the time-extended BKL process. That is, the Kasner stipulations corresponding to ???, taken as initial conditions, are at odds with the initial assumption imposed on Einstein’s field equations.

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Modeling in chaotic relativity

Cited by 39 publications

References 32 publications

Invariant Lyapunov exponents and chaos in cosmology

Invariant Lyapunov exponents and chaos in cosmology

Classical and Quantum Features of the Mixmaster Singularity

BKL Method in the Bianchi IX Universe Model Revisited

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