Covariance of the mixmaster chaoticity

Imponente, Giovanni; Montani, Giovanni

doi:10.1103/physrevd.63.103501

Cited by 54 publications

(71 citation statements)

References 20 publications

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“…Above we neglected the role of the potential because it influences the point-Universe evolution only via the bounces producing the establishment of a new free motion (for a detailed discussion about the chaotic properties of the random behavior that the point-universe performs in the potential, see [9,10,11]). This effect of the potential is summarized by the reflection law…”

Section: Generic Cosmological Modelmentioning

confidence: 99%

Classical and quantum behavior of the generic cosmological solution

Imponente¹,

Montani²

2006

AIP Conference Proceedings

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Abstract. In the present paper we generalize the original work of C.W. Misner [1] about the quantum dynamics of the Bianchi type IX geometry near the cosmological singularity. We extend the analysis to the generic inhomogeneous universe by solving the super-momentum constraint and outlining the dynamical decoupling of spatial points. Firstly, we discuss the classical evolution of the model in terms of the Hamilton-Jacobi approach as applied to the super-momentum and super-Hamiltonian constraints; then we quantize it in the approximation of a square potential well after an ADM reduction of the dynamics with respect to the super-momentum constraint only. Such a reduction relies on a suitable form for the generic three-metric tensor which allows the use of its three functions as the new spatial coordinates. We get a functional representation of the quantum dynamics which is equivalent to the Misner-like one when extended point by point, since the Hilbert space factorizes into ∞ 3 independent components due to the parametric role that the three-coordinates assume in the asymptotic potential term. Finally, we discuss the conditions for having a semiclassical behavior of the dynamics and we recognize that this already corresponds to having mean occupation numbers of order O(10 2 ).

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Section: Generic Cosmological Modelmentioning

confidence: 99%

Classical and quantum behavior of the generic cosmological solution

Imponente¹,

Montani²

2006

AIP Conference Proceedings

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“…There are two main aspects in chaos dynamics in general relativity. One is the evolution of the gravitational field itself, such as the evolution dynamics of cosmology models, especially the mixmaster universe model [2][3][4][5]. The other is the dynamics of test particles in known spacetime.…”

Section: Introductionmentioning

confidence: 99%

Revised research about chaotic dynamics in Mankoet al.spacetime

Han

2008

Phys. Rev. D

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A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that chaos phenomenon of test particles in gravitational field of rotating neutron stars which are described by Manko, Sanabria-Goméz, and Manko (Manko et al.) metric can only occur when the stars have oblate deformation. But the chaotic motions they found are limited in a very narrow zone which is very close to the center of the massive bodies. This paper argues that this is impossible because the region is actually inside of the stars, so the motions cannot exist at this place. In this paper, we scan all parameters space and find chaos and unstable fixed points outside of stars with big mass-quadrupole moments. The calculations show that chaos can only occur when the stars have prolate deformation. Because real deformation of stars should be oblate, all orbits of test particles around the rotating neutron stars described by Manko et al. solutions are regular. The case of nonzero dipolar magnetic moment has also been taken into account in this study.

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“…As well known (see [10]), the dynamics of the Bianchi type IX model, in terms of generic Misner-Chitrè-like (MCl) variables (τ, ξ, θ) and corresponding coniugate momenta, is summarized by the variational principle…”

Section: Statistical Mechanics Approachmentioning

confidence: 99%

“…being H a (a = l, m, n) the anisotropy parameters [10], such that the motion of the point Universe is restricted in the domain Γ H (see Figure 1). Such a dynamical scheme has the relevant feature to let free the choice of the lapse function unless explicitly chosen the form of the function Γ.…”

Section: Statistical Mechanics Approachmentioning

confidence: 99%

Mixmaster Chaoticity as Semiclassical Limit of the Canonical Quantum Dynamics

Imponente

Montani

2003

Int. J. Mod. Phys. D

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Within a cosmological framework, we provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt-DeserMisner approach, showing how the chaotic behavior characterizing the evolution of the system near the cosmological singularity can be obtained as the semiclassical limit of the canonical quantization of the model in the same dynamical representation. The relation between this intrinsic chaotic behavior and the indeterministic quantum dynamics is inferred through the coincidence between the microcanonical probability distribution and the semiclassical quantum one.

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Covariance of the mixmaster chaoticity

Cited by 54 publications

References 20 publications

Classical and quantum behavior of the generic cosmological solution

Classical and quantum behavior of the generic cosmological solution

Revised research about chaotic dynamics in Mankoet al.spacetime

Mixmaster Chaoticity as Semiclassical Limit of the Canonical Quantum Dynamics

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