Metric anisotropies and emergent anisotropic hydrodynamics

TL;DR

This paper derives expressions for energy-momentum tensor components in anisotropic space-times, showing their equivalence to anisotropic hydrodynamics results, and explores implications for Kasner metrics in Einstein's vacuum solutions.

Contribution

It provides a theoretical framework connecting anisotropic space-time metrics with anisotropic hydrodynamics, including derivations for Bianchi type I and Kasner metrics.

Findings

Energy-momentum tensor components match anisotropic hydrodynamics results.

Derived expressions for conserved quantities in anisotropic space-times.

Discussed implications for Kasner vacuum solutions in Einstein's equations.

Abstract

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.