Global properties of the solutions to the Einstein-Boltzmann system with cosmological constant in the Robertson-Walker space-time

Takou, Etienne

doi:10.4310/cms.2009.v7.n2.a6

Cited by 12 publications

(5 citation statements)

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“…the Boltzmann equation. For this case dust-like asymptotics have already been obtained in [21] for an isotropic spacetime with a cosmological constant and [10] provides a basis for a possible extension to the asymptotics in the case of Bianchi I with LRS symmetry. Finally we would like to mention that non-diagonal Bianchi I spacetimes are not only of interest in the context of cosmology, see for instance a recent work on the so called ultra-local limit [3].…”

Section: Discussionmentioning

confidence: 99%

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Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data

Nungesser

2010

Class. Quantum Grav.

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Assuming that the space-time is close to isotropic in the sense that the shear parameter is small and that the maximal velocity of the particles is bounded, we have been able to show that for non-diagonal Bianchi I-symmetric spacetimes with collisionless matter the asymptotic behaviour at late times is close to the special case of dust. We also have been able to show that all the Kasner exponents converge to 1 3 and an asymptotic expression for the induced metric has been obtained. The key was a bootstrap argument.The sign conventions of [18] are used. In particular, we use metric signature -+ + + and geometrized units, i.e. the gravitational constant G and the speed of light c are set equal to one. Also the Einstein summation convention that repeated indices are to be summed over is used. Latin indices run from one to three. C will be an arbitrary constant and ǫ will denote a small and strictly positive constant. They both may appear several times in different equations or inequalities without being the same constant. A dot above a letter will denote a derivative with respect to the cosmological (Gaussian) time t.We will use the 3+1 decomposition of the Einstein equations as made in [18]. We use Gauss coordinates, which implies that the lapse function is the identity and the shift vector vanishes, so comparing our metric with (2.28) of [18] we have that α = 1 and β a = 0. The

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Section: Discussionmentioning

confidence: 99%

“…the Boltzmann equation. For this case, dust-like asymptotics have already been obtained in [21] for an isotropic spacetime with a cosmological constant and a basis is provided for a possible extension to the asymptotics in the case of Bianchi I with LRS symmetry in [10].…”

Section: Discussionmentioning

confidence: 99%

Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data

Nungesser

2010

Class. Quantum Grav.

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“…Local existence was proved by Bancel and Choquet-Bruhat many years ago under a 'µ − N ' regularity assumption [1,2]. Noutchegueme, Takou and Dongo studied the Boltzmann equation in some cosmological settings with certain assumptions on scattering kernels close to µ − N regularity [15][16][17]21]. The limits of the µ − N regularity assumption lie in the fact that it is just a mathematical assumption which can not be interpreted physically.…”

Section: Introductionmentioning

confidence: 99%

The relativistic Boltzmann equation on a spherically symmetric gravitational field

Takou

Ciake

2017

Class. Quantum Grav.

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In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. We consider this equation on a spherically symmetric gravitational field spacetime. The collision kernel considered here is for the hard potentials case. We prove the existence of a unique global (in time) mild solution in a suitable weighted space.

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“…After establishing global existence of the solution for the Einstein equation coupled to various field equations, one of the main problems is the properties of these solutions. This has been done in [11] by E. Takou in the case of Einstein-Boltzmann with Robertson-Walker space-time background; in [12] by H. Lee who studied asymptotic behaviour of the Einstein-Vlasov system with positive cosmological constant; in [4] by N. Noutchegueme and A. Nangue who studied the case of coupled Einstein-Maxwell-Massive scalar field with cosmological constant, but they did not consider the Boltzmann equation which introduce in the sources term of the Einstein equation the tensor…”

Section: Introductionmentioning

confidence: 99%

Global Properties of the Solution of the Einstein-Maxwell-Boltzmann-Scalar Field System with Pseudo-Tensor of Pressure on a Bianchi Type I Space-Time

Norbert¹,

David²,

Etienne³

2017

GLM

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Abstract. In this paper, we study the asymptotic behaviour, the geodesic completeness and the energy condition for the coupled Einstein-Maxwell-Boltzmann-Massive scalar field system with pseudo-tensor of pressure in the sources which rules the dynamincs of kind of charged pure matter in the presence of a massive scalar field which is a continuity of the work we have done. We then prove that, at late times, the Hubble variable of the space time goes to strictly positive limit.

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Global properties of the solutions to the Einstein-Boltzmann system with cosmological constant in the Robertson-Walker space-time

Abstract: Abstract. We study the global properties of the solutions for the initial value problem for the Einstein-Boltzmann system with positive cosmological constant and arbitrarily large initial data, in the spatially homogeneous case, in a Robertson-Walker space-time.

Cited by 12 publications

References 4 publications

Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data

Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data

The relativistic Boltzmann equation on a spherically symmetric gravitational field

Global Properties of the Solution of the Einstein-Maxwell-Boltzmann-Scalar Field System with Pseudo-Tensor of Pressure on a Bianchi Type I Space-Time

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