Propagation of hydromagnetic waves in a relativistic plasma

The hydrodynamic approach to a relativistic gas is studied on the basis of methods used by Chew, Goldberger & Low and by Scargle. As the result of this study, the explicit form of the energy-momentum tensor is obtained by straight-forward application of Lorentz transformation. The term corresponding to non-zero momentum density in the plasma frame of reference is included in the energy-momentum tensor. For the limiting case of small bulk velocities compared with the speed of light in vacua, the energy flux as described by non- relativistic theory is immediately recovered. For the special case of scalar pressure, the energy-momentum tensor considered by Taub and by Harris follows directly from our expression. In a small-perturbation approximation, it is possible to close the system of MHD equations. As a result the solution describing all possible wave modes is derived. This solution coincides with the solution obtained by means of the kinetic theory.