Expansion of a locally equilibrated fluid is considered in an anisotropic space-time given by Bianchi type I metric. Starting from an isotropic equilibrium phase-space distribution function in the local rest frame, we obtain expressions for thermodynamic quantities 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.
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