Anisotropic matching principle for the hydrodynamics expansion

TL;DR

This paper introduces a new anisotropic hydrodynamics expansion that exactly incorporates momentum anisotropies at leading order, improving the description of systems with large pressure anisotropies.

Contribution

It proposes a general prescription for hydrodynamics expansion around an anisotropic background, directly deriving pressure correction dynamics from the Boltzmann equation.

Findings

Achieves unprecedented agreement with exact Boltzmann solutions in the Bjorken limit.

Allows large pressure anisotropies without next-to-leading order corrections.

Provides a more accurate hydrodynamic description of anisotropic systems.

Abstract

Following the recent success of anisotropic hydrodynamics we propose a new, general prescription for the hydrodynamics expansion around an anisotropic background. The anisotropic distribution is fixing exactly the complete energy-momentum tensor, just like the effective temperature is fixing the proper energy density in the ordinary expansion around local equilibrium. This means that momen- tum anisotropies are already included at the leading order, allowing for large pressure anisotropies without the need of a next to leading order treatment. The first moment of the Boltzmann equation (local four-momentum conservation) provides the time evolution of the proper energy density and the four velocity. Differently from previous prescriptions, the dynamic equations for the pressure corrections are not derived from the zeroth or second moment of the Boltzmann equation, but they are taken directly from the exact evolution given by the Boltzmann equation. We check the effec- tiveness of this new approach by matching with the exact solution of the Boltzmann equation in the Bjorken limit with the collisional kernel treated in relaxation time approximation, finding an unprecedented agreement.