Relativistic heat conduction: the kinetic theory approach and comparison with Marle's model

In order to close the set of relativistic hydrodynamic equations, constitutive relations for the dissipative fluxes are required. In this work we outline the calculation of the corresponding closure for the heat flux in terms of the gradients of the independent scalar state variables: number density and temperature. The results are compared with the ones obtained using Marle's approximation in which a relativistic correction factor is included for the relaxation time parameter. It is shown how including such correction this BGK-like model yields good results in the relativistic case and not only in the non-relativistic limit as was previously found by other authors.