  We consider the evolution of a system of chargeless and massless particles in
an anisotropic space-time given by the Bianchi type I metric. Specializing to
the axis-symmetric case, we derive the framework of anisotropic hydrodynamics
from the Boltzmann equation in the relaxation-time approximation. We consider
the case of the axis-symmetric Kasner metric and study the approach to the
emergent attractor in near and far-off-equilibrium regimes. Further, by
relaxing the Kasner conditions on metric coefficients, we study the effect of
expansion geometries on the far-off-equilibrium attractor and discuss its
implications in the context of relativistic heavy-ion collisions.
