A gas of hard spheres expanding in Bjorken flow has a constant Knudsen number, which yields an exact analytical hydrodynamic attractor and the first convergent gradient expansion in an expanding relativistic system.
We start our analysis by investigating the hydrodynamic regime of Israel-Stewart-like theories [40–42] derived from the Boltzmann equation
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Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
A gas of hard spheres expanding in Bjorken flow has a constant Knudsen number, which yields an exact analytical hydrodynamic attractor and the first convergent gradient expansion in an expanding relativistic system.