  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.
