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.

• Received 19 August 2009

DOI:https://doi.org/10.1103/PhysRevC.81.041901