Generic instabilities in first-order dissipative relativistic fluid theories

We consider the stability of a general class of first-order dissipative relativistic fluid theories which includes the theories of Eckart and of Landau and Lifshitz as special cases. We show that all of these theories are unstable in the sense that small spatially bounded departures from equilibrium at one instant of time will diverge exponentially with time. The time scales for these instabilities are very short; for example, water at room temperature and pressure has an instability with a growth time scale of about 10^-34 seconds in these theories. These results provide overwhelming motivation (we believe) for abandoning these theories in favor of the second-order (Israel) theories which are free of these difficulties.