Shock waves in strongly coupled plasmas

TL;DR

This paper investigates shock waves in strongly coupled N=4 supersymmetric Yang-Mills plasma using holography, deriving properties of weak and strong shocks through gravity duals and comparing with hydrodynamic models.

Contribution

It provides a dual gravity description of both weak and strong shock waves in strongly coupled plasmas, revealing differences from hydrodynamic approximations.

Findings

Weak shocks are described by a derivative expansion of the dual metric.

Strong shocks exhibit an exponential tail with a width scaling as (1-v^2)^{1/4}.

Hydrodynamics and Israel-Stewart models agree for weak shocks but not for strong shocks.

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 $v\to 1$ the penetration depth $\ell$ scales as $\ell\sim (1-v^2)^{1/4}$. We compare the results with second order hydrodynamics and the Israel-Stewart 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.