Relativistic dissipative hydrodynamics and the nuclear equation of state

The theory of dissipative, relativistic fluids due to Israel and Stewart is used to constrain the form of the nuclear equation of state. In the Israel-Stewart theory, there are conditions on the equation of state and other thermodynamic properties (the ``second-order'' coefficients) of a fluid which, if satisfied, guarantee that equilibria are stable and that fluid perturbations propagate causally and obey hyperbolic equations. The second-order coefficients in the Israel-Stewart theory, which are relaxation times for the dissipative degrees of freedom and coupling constants between different forms of dissipation, are derived for a free, degenerate Fermi gas. It is shown rigorously that the free, degenerate Fermi gas is stable (and hence causal) at all temperatures in this theory. These values for the second-order coefficients are then used in the stability conditions to constrain various proposed expressions for the nuclear ground-state energy. The stability conditions are found to provide significantly more stringent constraints on the proposed equations of state than the usual simple restriction that the adiabatic sound speed be less than the speed of light.