Analytic approach to the relaxation time approximation Boltzmann attractor

We reformulate the Boltzmann equation in the relaxation time approximation undergoing Bjorken flow in terms of a novel partial differential equation for the generating function of the moments of the distribution function. This is used to obtain a series expansion of this system's far-from-equilibrium attractor. This expansion possesses a finite radius of convergence, which proves the existence of the attractor. Furthermore, the series can be analytically continued to late times and we find that this procedure reproduces the known values of shear viscosity and other transport coefficients to high accuracy. We also provide a simple approximate analytic expression that describes the attractor in the entire domain of interest for studies of quark-gluon plasma dynamics.