Figure 2: Graphical solution in the -plane (upper panel) and in the -plane (lower panel) of the relativistic Riemann problem with initial data  = 1.0,  = 1.0,  = 0.0, and  = 0.1,  = 0.125,  = 0.0 for different values of the tangential velocity  = 0, 0.5, 0.9, 0.999, represented by solid, dashed, dashed-dotted and dotted lines, respectively. An ideal gas EOS with  = 1.4 was assumed. The crossing point of any two lines in the upper panel gives the pressure and the normal velocity in the intermediate states. The value of the tangential velocity in the states and is obtained from the value of the corresponding functions at in the lower panel, and gives the solution for vanishing tangential velocity. The range of possible solutions is given by the shaded region in the upper panel.