- Published on 10 August 2012
What is the general relativistic version of the Navier-Stokes-Fourier dissipative hydrodynamics? Surprisingly, no satisfactory answer to this question is known today. Eckart's early solution [Eckart, Phys. Rev. 58, 919 (1940)], is considered outdated on many grounds: the instability of its equilibrium states, ill-posed initial-value formulation, inconsistency with linear irreversible thermodynamics, etc. Although alternative theories have been proposed recently, none appears to have won the consensus. This paper reconsiders the foundations of Eckart's theory, focusing on its main peculiarity and simultaneous difficulty: the “inertia of heat” term in the constitutive relation for the heat flux, which couples temperature to acceleration. In particular, it shows that this term arises only if one insists on defining the thermal diffusivity independently of the gravitational field. It is argued that this is not a physically sensible approach, because gravitational time dilation implies that the diffusivity actually varies in space. In a nutshell, where time runs faster, thermal diffusion also runs faster. It is proposed that this is the physical meaning of the “inertia of heat” concept, and that such an effect should be expected in any theory of dissipative hydrodynamics that is consistent with general relativity.