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  The Einstein-Boltzmann system and positivity

Lee, H., & Rendall, A. D. (2013). The Einstein-Boltzmann system and positivity. Journal of hyperbolic differential equations, 77(1), 77-104. doi:10.1142/S0219891613500033.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-4D9D-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-4DA1-1
Genre: Journal Article

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1203.2471 (Preprint), 285KB
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 Creators:
Lee, Ho1, Author              
Rendall, Alan D.1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
 Abstract: The Einstein-Boltzmann system is studied, with particular attention to the non-negativity of the solution of the Boltzmann equation. A new parametrization of post-collisional momenta in general relativity is introduced and then used to simplify the conditions on the collision cross-section given by Bancel and Choquet-Bruhat. The non-negativity of solutions of the Boltzmann equation on a given curved spacetime has been studied by Bichteler and by Tadmon. By examining to what extent the results of these authors apply in the framework of Bancel and Choquet-Bruhat, the non-negativity problem for the Einstein-Boltzmann system is resolved for a certain class of scattering kernels. It is emphasized that it is a challenge to extend the existing theory of the Cauchy problem for the Einstein-Boltzmann system so as to include scattering kernels which are physically well-motivated.

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 Dates: 2012-03-1220122012-06-012013
 Publication Status: Published in print
 Pages: 24 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1203.2471
DOI: 10.1142/S0219891613500033
 Degree: -

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Title: Journal of hyperbolic differential equations
Source Genre: Journal
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Publ. Info: N.J. : World Scientific
Pages: - Volume / Issue: 77 (1) Sequence Number: - Start / End Page: 77 - 104 Identifier: ISSN: 0219-8916
CoNE: /journals/resource/111081782435004