Remarks on relativistic kinetic theory to first order in the gradients

In this paper we emphasize some conceptual points related to the kinetic foundations of relativistic hydrodynamics. We summarize previous work and focus on the construction of the heat flux from a kinetic theory point of view. A thorough discussion addressing aspects concerning stability and causality under linear perturbations, and the construction of an appropriate stress-energy tensor, in the case of a high temperature (special relativistic) single component dilute fluid is included.