Extensivity of irreversible current and stability in causal dissipative hydrodynamics

We extended our formulation of causal dissipative hydrodynamics (Koide et al 2007 Phys. Rev. C 75 034909) to be applicable to the ultra-relativistic regime by considering the extensiveness of irreversible currents. The new equation has a nonlinear term which suppresses the effect of viscosity. We found that such a term is essential to guarantee the positive definiteness of the inertia term and to stabilize numerical calculations in ultra-relativistic initial conditions. Because of the suppression of the viscosity, the behavior of the fluid is more close to that of the ideal fluid. Our result is essentially the same as that from the extended irreversible thermodynamics, but is different from the Israel-Stewart theory. A possible origin of the difference is discussed.