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Abstract: Shock waves are supersonic disturbances propagating in a fluid and givingrise to dissipation and drag. Weak shocks, i.e., those of small amplitude, canbe well described within the hydrodynamic approximation. On the other hand,strong shocks are discontinuous within hydrodynamics and therefore probe themicroscopics of the theory. In this paper we consider the case of the stronglycoupled N=4 plasma whose microscopic description, applicable for scales smallerthan the inverse temperature, is given in terms of gravity in an asymptotically$AdS 5$ space. In the gravity approximation, weak and strong shocks should bedescribed by smooth metrics with no discontinuities. For weak shocks we findthe dual metric in a derivative expansion and for strong shocks we uselinearized gravity to find the exponential tail that determines the width ofthe shock. In particular we find that, when the velocity of the fluid relativeto 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 secondorder hydrodynamics and the Israel-Stewart approximation. Although they allagree in the hydrodynamic regime of weak shocks, we show that there is not evenqualitative agreement for strong shocks. For the gravity side, the existence ofshock waves implies that there are disturbances of constant shape propagatingon the horizon of the dual black holes.



Author: Sergei Khlebnikov, Martin Kruczenski, Georgios Michalogiorgakis

Source: https://arxiv.org/







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