(3+1)-dimensional framework for leading-order non conformal anisotropic hydrodynamics

TL;DR

This paper introduces a comprehensive (3+1)-dimensional anisotropic hydrodynamics framework for massive particles, capturing large pressure anisotropies and transverse dynamics, and aligns with second-order viscous hydrodynamics near equilibrium.

Contribution

It develops a novel (3+1)-dimensional anisotropic hydrodynamics model that explicitly includes momentum anisotropy and couples shear and bulk pressures, extending previous approaches.

Findings

Framework captures large pressure anisotropies.

Close-to-equilibrium limit matches second-order viscous hydrodynamics.

Coupling between shear and bulk corrections remains significant.

Abstract

In this work I develop a new framework for anisotropic hydrodynamics that generalizes the leading order of the hydrodynamic expansion to the full (3+1)-dimensional anisotropic massive case. Following previous works, my considerations are based on the Boltzmann kinetic equation with the collisional term treated in the relaxation time approximation. The momentum anisotropy is included explicitly in the leading term, allowing for a large difference between the longitudinal and transverse pressures as well as for non trivial transverse dynamics. Energy and momentum conservation is expressed by the first moment of the Boltzmann equation. The system of equations is closed by using the zeroth and second moments of the Boltzmann equation. The close-to-equilibrium matching with second-order viscous hydrodynamics is demonstrated. In particular, I show that the coupling between shear and bulk pressure corrections, recently proved to be important for an accurate description of momentum anisotropy and bulk viscous dynamics, does not vanish in the close-to-equilibrium limit.