We compute the moments of the nonlinear binary collision integral in the
ultrarelativistic hard-sphere approximation for an arbitrary anisotropic
distribution function in the local rest frame. This anisotropic distribution
function has an angular asymmetry controlled by the parameter of anisotropy
$\xi$, such that in the limit of a vanishing anisotropy $\lim_{\xi \rightarrow
0} \hat{f}_{0 \mathbf{k}} = f_{0 \mathbf{k}}$, approaches the spherically
symmetric local equilibrium distribution function. The corresponding moments of
the binary collision integral are obtained in terms of quadratic products of
different moments of the anisotropic distribution function and couple to a well
defined set of lower-order moments. To illustrate these results we compare the
moments of the binary collision integral to the moments of the widely used
relaxation-time approximation of Anderson and Witting in case of a spheroidal
distribution function. We found that in an expanding system the nonlinear
Boltzmann collision term leads to twice slower equilibration than the
relaxation-time approximation. Furthermore we also show that including two
dynamical moments helps to resolve the ambiguity which additional moment of the
Boltzmann equation to choose to close the conservation laws.

Cet article explore les excursions dans le temps et leurs implications.

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