The equations of hydrodynamics for a thermally conducting, viscous, compressible fluid in special relativity

In this paper the equations of hydrodynamics governing the behavior of a thermally conducting, viscous, compressible fluid in special relativity are derived. We also derive the expressions (expansion, rotation, and shear) describing the kinematics of the fluid as seen by an observer comoving with an element of the fluid and employing three Fermi-transported, local, Cartesian axes. It is furthermore observed that there is the possibility for waves of viscosity to exist in the fluid, and we determine, in the case of one-dimensional flow, the condition for the existence of these waves.