Shock Wave Collisions and Thermalization in AdS_5

TL;DR

This paper investigates heavy ion collisions at strong coupling via AdS/CFT, constructing shock wave metrics in AdS_5, analyzing energy-momentum tensors, and demonstrating black hole formation indicating thermalization.

Contribution

It provides an analytic perturbative construction of shock wave collisions in AdS_5 and links shock stopping to nuclear stopping and thermalization in the dual field theory.

Findings

Shock waves stop immediately after collision in AdS_5.

Energy-momentum tensor indicates non-ideal hydrodynamics.

Black hole formation proves thermalization at strong coupling.

Abstract

We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. According to the AdS/CFT dictionary heavy ion collisions correspond to gravitational shock wave collisions in AdS_5. We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS_5, which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling.