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Journal Article

The Einstein-Boltzmann system and positivity

MPS-Authors
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Lee,  Ho
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1203.2471
(Preprint), 285KB

S0219891613500033.pdf
(Any fulltext), 403KB

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Citation

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.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-4D9D-D
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.