In the collapsar model of long GRBs the jet is formed at the center of the progenitor
star, propagates in its interior, and produces the observed gamma rays much after its
breakout from the star. The loss of pressure support during breakout induces a strong
rarefaction wave that propagates inside the jet and causes its bulk acceleration. This
mechanism has been already studied using axisymmetric magnetohydrodynamic (MHD)
simulations assuming a prescribed shape for the surface between the jet and its
environment, as well as using simple rarefaction waves in planar geometry. Trying to
improve over these works, we solve the steady-state, axisymmetric, relativistic MHD
equations using the method of characteristics. In this way the jet boundary is found
self-consistently and the rarefaction wave is studied in the axisymmetric geometry. In
this poster we present our first results and a comparison with previous works.