• Corpus ID: 17043947

Global existence of solutions for the Einstein-Boltzmann system with cosmological constant in the Robertson-Walker space-time for arbitrarily large initial data

@article{Takou2006GlobalEO,
  title={Global existence of solutions for the Einstein-Boltzmann system with cosmological constant in the Robertson-Walker space-time for arbitrarily large initial data},
  author={Etienne Takou and Norbert Noutchegueme},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2006}
}
  • E. Takou, N. Noutchegueme
  • Published 3 January 2006
  • Mathematics, Physics
  • arXiv: General Relativity and Quantum Cosmology
We prove a global in time existence theorem 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. 

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References

SHOWING 1-10 OF 24 REFERENCES

Global existence of solutions for the relativistic Boltzmann equation with arbitrarily large initial data on a Bianchi Type I space-time

We prove, for the relativistic Boltzmann equation on a Bianchi Type I space-time, a global existence and uniqueness theorem, for arbitrarily large initial data.

Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the

Local Existence and Continuation Criterion for Solutions of the Spherically Symmetric Einstein-Vlasov-Maxwell System

Using the iterative scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation

Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case

where R(t) > 0 and the distribution function f(t, x, p) does not depend on x and depends only on p = |p| (f(t, x, p) = f(t, p)). We consider the initial value problem in such a case. The aim of this

The nature of singularities in plane symmetric scalar field cosmologies

The nature of the initial singularity in spatially compact plane symmetric scalar field cosmologies is investigated. It is shown that this singularity is crushing and velocity dominated and that the

The Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model.

Differentiability of spatially homogeneous solutions of the Boltzmann equation in the non maxwellian case

The non linear Boltzmann equation is studied and differentiable solutions are shown to exist if the initial datum is suitably chosen

Asymptotic stability of the relativistic Maxwellian

Solutions of the relativistic Boltzmann equation are studied for all initial data which are periodic in the space variable and near equilibrium. An equilibrium is a relativistic Maxwellian

Survey of General Relativity Theory

TLDR
The purpose of these lectures was to give a survey of Einstein’s theory of gravitation and the connection between physical and mathematical concepts and ideas.

The Large Scale Structure of Space-Time

TLDR
The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.