Stability and Causality in relativistic dissipative hydrodynamics

Understand

The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed.

• We show that the problem 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.