Stability and causality in dissipative relativistic fluids

Abstract

The standard theory of relativistic dissipative fluid mechanics developed by Eckart contains several undesirable features: thermal and viscous fluctuations propagate acausally; there exist generic short wavelength secular instabilities; and there is not a well posed initial value problem for rotating fluids. In this paper we examine whether the generalization of Eckart's theory developed by Israel has succeeded in eliminating these features. We first generalize Israel's theory to include the possibility of nonuniform equilibrium configurations. This generalization allows us to describe equilibrium configurations which may be rotating and self-gravitating such as neutron stars. We then evaluate the stability conditions for these fluids and compute the characteristic velocities at which perturbations propagate. Our main result is that if these fluids are stable, then the characteristic velocities are subluminal and the perturbations propagate via hyperbolic equations. Thus Israel's theory is causal for all stable fluids. In addition, there is no generic instability, and the initial value problem is well posed. In our opinion, for these reasons, Israel's theory should replace Eckart's as the standard theory of relativistic dissipative fluid mechanics.