Full analytical ultrarelativistic 1D solutions of a planar working surface

ABSTRACT We show that the 1D planar ultrarelativistic shock tube problem with an polytropic equation of state can be solved analytically for case a working surface, i.e. when initial discontinuity on hydrodynamical quantities form two waves separating from contact discontinuity. The procedure is based extensive use Taub jump conditions relativistic waves, adiabatic, and performing Lorentz transformations to present solution in system reference adequate external observer at rest. solutions are found using set very useful theorems related factors transforming between systems reference. energy dissipated inside surface relevant studies light curves observed astrophysical jets so, we provide full analytical this phenomenon assuming periodic velocity injected base jet.