  Expansion of a locally equilibrated fluid is considered in an anisotropic
space-time given by Bianchi type I metric. Starting from isotropic equilibrium
phase-space distribution function in the local rest frame, we obtain
expressions for components of the energy-momentum tensor and conserved current,
such as number density, energy density and pressure components. In the case of
an axis-symmetric Bianchi type I metric, we show that they are identical to
that obtained within the setup of anisotropic hydrodynamics. We further
consider the case when Bianchi type I metric is a vacuum solution of Einstein
equation: the Kasner metric. For axis-symmetric Kasner metric, we discuss the
implications of our results in the context of anisotropic hydrodynamics.
