Abstract
We derive the existence conditions for relativistic shock waves propagating in a perfectly conducting fluid with a general equation of state that guarantees that the stationary wave has a continuous profile in the presence of weak viscosity. To this end we study the one-dimensional solutions of the magnetohydrodynamic equations with a relativistic viscosity tensor. We allow for anomalous regions of thermodynamic variables and do not use the well-known condition for the convexity of Poisson adiabats. The results lead to relationships among the velocities of magnetoacoustic, Alfven, and shock waves in front of and behind the discontinuity that prove to be more stringent than the corollaries of the evolution conditions. In the nonrelativistic case and in parallel and perpendicular shock waves, any difference between the two conditions disappears.
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