Stability and causality in relativistic dissipative hydrodynamics

The stability and causality of the Landau–Lifshitz theory and the Israel–Stewart-type causal dissipative hydrodynamics are discussed. We show that the problems of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.