Comparison between variational and traditional approaches to relativistic thermodynamics of dissipative fluids

The variational formalism recently developed by Carter is analyzed in the special case for which a viscous fluid is described by means of an entropy current, a particle current, and one viscosity tensor, and is matched with the well-known Israel-Stewart theory of dissipative fluids. It is shown that the deductive variational formalism and the phenomenological theory developed by Israel and Stewart are not equivalent, but constitute two members of a more general family of theories. Relations between the main parameters of these two theories are set. The equations of motion are compared. Perturbations about an equilibrium state and the associated characteristic surfaces of the formalisms are studied; in this particular case, the Carter and the Israel-Stewart theories are shown to coincide, particularly as far as their causality properties are concerned.