A consistent first-order model for relativistic heat flow
  This paper revisits the problem of heat conduction in relativistic fluids,
associated with issues concerning both stability and causality. It has long
been known that the problem requires information involving second order
deviations from thermal equilibrium. Basically, any consistent first-order
theory needs to remain cognizant of its higher-order origins. We demonstrate
this by carrying out the required first-order reduction of a recent variational
model. We provide an analysis of the dynamics of the system, obtaining the
conditions that must be satisfied in order to avoid instabilities and acausal
signal propagation. The results demonstrate, beyond any reasonable doubt, that
the model has all the features one would expect of a real physical system. In
particular, we highlight the presence of a second sound for heat in the
appropriate limit. We also make contact with previous work on the problem by
showing how the various constraints on our system agree with previously
established results.
