Shocks in quark-gluon plasmas

Hydrodynamics is known to well describe matter created in high-energy heavy-ion collisions. Large depositions of energy by passing jets should create not only the sound waves, already discussed in the literature, but also shock waves of finite amplitude. This paper is an introduction to relativistic shocks, which go through elementary energy and momentum continuity arguments, to weak shocks treated in the Navier-Stokes approximation to out-of-equilibrium settings of anti de Sitter/conformal field theory. While we have not yet found numerical solutions to corresponding Einstein equations, we have found a variational approximation to the sum of their squares. Our general conclusion is that deviations from Lublinsky-Shuryak and Navier-Stokes hydrodynamical shock profiles are surprisingly small, even for strong shocks. We end with a list of open questions which the exact solution should be able to answer.