Third-order relativistic dissipative hydrodynamics

TL;DR

This paper extends relativistic dissipative hydrodynamics to third order in shear stress, deriving new evolution equations and demonstrating their improved accuracy in modeling viscous relativistic fluids.

Contribution

The paper introduces a third-order expansion of the entropy current and derives a novel evolution equation for shear stress in relativistic hydrodynamics.

Findings

Third-order corrections significantly improve agreement with kinetic transport results.

Higher-order terms are crucial for accurately modeling highly viscous fluids.

Scaling solutions match well with kinetic calculations across different viscosity ratios.

Abstract

Following the procedure introduced by Israel and Stewart, we expand the entropy current up to the third order in the shear stress tensor $\pi^{\alpha\beta}$ and derive a novel third-order evolution equation for $\pi^{\alpha\beta}$. This equation is solved for the one-dimensional Bjorken boost-invariant expansion. The scaling solutions for various values of the shear viscosity to the entropy density ratio $\eta/s$ are shown to be in very good agreement with those obtained from kinetic transport calculations. For the pressure isotropy starting with 1 at $\tau_0=0.4 fm/c$, the third-order corrections to Israel-Stewart theory are approximately 10\% for $\eta/s=0.2$ and more than a factor of 2 for $\eta/s=3$. We also estimate all higher-order corrections to Israel-Stewart theory and demonstrate their importance in describing highly viscous matters.