[RicardoGoncalves]

Hi,
I have been struggling to understand a specific part of the derivation of the exact Riemann solver for the Euler equations presented in Toro's book (Riemann Solvers and Numerical Methods for Fluid Dynamics).
The particular issue starts on page 119, where the author presents the generic equation connecting two states (L and R), the iterative solution of which provides the value of p* (the pressure in the star region). The functions that appear in this equation depend on whether the wave is a shock or a rerafaction wave, but this is intriguingly defined by the condition that p*>pL or p*<pL (for example for the left wave, equation 4.6). In my understanding what defines a shock (or a rarefaction) is the convergance (divergence) of the eigenvectors, rather than the pressure.
I would very much appreciate your help with this.
Thanks,
Ricardo