Dissipative properties of relativistic fluids in a general curved space–time

Abstract

Dissipative force–flux relations are established in a strict covariant fashion for a relativistic fluid in a general curved space–time within the framework of kinetic theory. The Boltzmann equation is addressed to first order in the gradients by employing the Chapman–Enskog expansion and the corresponding constitutive equations are derived by considering a relaxation approximation. It is shown that in the heat flux, only the corresponding transport coefficient is modified when the gradients of the state variables are considered as the thermodynamic forces. On the other hand, the viscous terms features new driving terms due to the curvature of space–time that only vanish in particular cases.