Shock waves in strongly coupled plasmas
Abstract
Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong shocks are discontinuous within hydrodynamics and therefore probe the microscopics of the theory. In this paper, we consider the case of the strongly coupled N=4 plasma whose microscopic description, applicable for scales smaller than the inverse temperature, is given in terms of gravity in an asymptotically AdS_{5} space. In the gravity approximation, weak and strong shocks should be described by smooth metrics with no discontinuities. For weak shocks, we find the dual metric in a derivative expansion, and for strong shocks we use linearized gravity to find the exponential tail that determines the width of the shock. In particular, we find that, when the velocity of the fluid relative to the shock approaches the speed of light v→1 the penetration depth ℓ scales as ℓ∼(1v^{2})^{1/4}. We compare the results with secondorder hydrodynamics and the IsraelStewart approximation. Although they all agree in the hydrodynamic regime of weak shocks, we show that there is not even qualitative agreement for strong shocks. For the gravity side, the existence of shock waves implies that there are disturbances of constant shape propagating on the horizon of the dual black holes.
 Publication:

Physical Review D
 Pub Date:
 December 2010
 DOI:
 10.1103/PhysRevD.82.125003
 arXiv:
 arXiv:1004.3803
 Bibcode:
 2010PhRvD..82l5003K
 Keywords:

 12.38.Mh;
 04.70.Bw;
 Quarkgluon plasma;
 Classical black holes;
 High Energy Physics  Theory;
 Nuclear Theory
 EPrint:
 47 pages, 8 figures