Abstract
Following the procedure introduced by Israel and Stewart, we expand the entropy current up to the third order in the shear stress tensor ${\ensuremath{\pi}}^{\ensuremath{\alpha}\ensuremath{\beta}}$ and derive a novel third-order evolution equation for ${\ensuremath{\pi}}^{\ensuremath{\alpha}\ensuremath{\beta}}$. 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 $\ensuremath{\eta}/s$ are shown to be in very good agreement with those obtained from kinetic transport calculations. For the pressure isotropy starting with 1 at ${\ensuremath{\tau}}_{0}=0.4$ fm/$c$, the third-order corrections to Israel-Stewart theory are approximately $10%$ for $\ensuremath{\eta}/s=0.2$ and more than a factor of 2 for $\ensuremath{\eta}/s=3$. We also estimate all higher-order corrections to Israel-Stewart theory and demonstrate their importance in describing highly viscous matters.
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