Shock waves in strongly coupled plasmas II

Abstract

In a recent paper we have analyzed the AdS/CFT duals to shock waves propagating in the N=4 plasma. Here we study further properties of the system. In the gravity description we consider the properties of the dual black holes, showing in particular that they are stationary black holes with expanding horizons. This is possible because the horizon is not compact; in the fluid, this corresponds to the situation when entropy is being produced and carried away to infinity. We also consider shocks in dimensionalities d other than four and find that, for plasmas whose duals are given by asymptotically AdS spaces, the exponential tail of the shock on the supersonic side shrinks as gamma^(-2/d) as the velocity approaches the speed of light (the Lorentz factor gamma goes to infinity). This generalizes the behavior gamma^(-1/2) we have found previously for d=4. Finally, we consider corrugations of the shock front and show that the shock is stable under such perturbations. There are, however, long lived modes, excitations of which describe generation of sound by the shock wave, the energy for this being provided by the incoming fluid.