The Einstein-Boltzmann system and positivity

Details The Einstein-Boltzmann system and positivity The Einstein-Boltzmann system and positivity

2012-03-12

arxiv.org/abs/1203.2471v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages

Scientific paper

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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