Using gauge/gravity duality, we study the creation and evolution of anisotropic, homogeneous strongly coupled N = 4 supersymmetric Yang-Mills plasma. In the dual gravitational description, this corresponds to horizon formation in a geometry driven to be anisotropic by a time-dependent change in boundary conditions.Introduction.-The realization that the quark-gluon plasma (QGP) produced at RHIC is strongly coupled [1] has prompted much interest in the study of strongly coupled non-Abelian plasmas. Hydrodynamic simulations of heavy ion collisions have demonstrated that the QGP produced at RHIC is well modeled by near-ideal hydrodynamics [2], which is a signature of a strongly coupled system. The success of hydrodynamic modeling of RHIC collisions suggests that the produced plasma locally isotropizes over a time scale τ iso 1 fm/c [3] . Understanding the dynamics responsible for such rapid isotropization in a far-from-equilibrium nonAbelian plasma is a challenge.Because of the difficulty in studying real time dynamics in QCD at strong coupling, it is useful to have a toy model where one can study the dynamics of a far from equilibrium, strongly coupled non-Abelian plasma in a controlled setting. One such toy model is strongly coupled N = 4 supersymmetric Yang-Mills theory (SYM), where one can use gauge/gravity duality to study the theory in the limit of large N c and large 't Hooft coupling λ. This has motivated much work devoted to studying various non-equilibrium properties of thermal SYM plasma.We are interested in exploring the physics of isotropization in far-from-equilibrium non-Abelian plasmas, in the simplest setting which allows complete theoretical control. This leads us to focus on the dynamics of homogeneous, but anisotropic, states in strongly coupled, large N c SYM. A conceptually simple way to create nonequilibrium states is to turn on time-dependent background fields coupled to operators of interest. To create states in which the stress tensor is anisotropic, it is natural to consider the response of the theory to a timedependent change in the spatial geometry. For simplicity, we limit attention to geometries which have spatial homogeneity (i.e., translation invariance in all spatial directions), an O(2) rotation invariance, and a constant spatial volume element. The most general metric satisfying these conditions may be written as

Using holography, we study the collision of planar shock waves in strongly coupled N = 4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.Introduction.-The recognition that the quark-gluon plasma (QGP) produced in relativistic heavy ion collisions is strongly coupled [1], combined with the advent of gauge/gravity duality (or "holography") [2,3], has prompted much work exploring both equilibrium and non-equilibrium properties of strongly coupled N = 4 supersymmetric Yang-Mills theory (SYM), which may be viewed as a theoretically tractable toy model for real QGP. Multiple authors have discussed collisions of infinitely extended planar shock waves in SYM, which may be viewed as instructive caricatures of collisions of large, highly Lorentz-contracted nuclei. In the dual description of strongly coupled (and large N c ) SYM, this becomes a problem of colliding gravitational shock waves in asymptotically anti-de Sitter (AdS 5 ) spacetime. Previous work has examined qualitative properties and trapped surfaces [4][5][6][7], possible early time behavior [8][9][10], and expected late time asymptotics [11,12]. As no analytic solution is known for this gravitational problem, solving the gravitational initial value problem numerically is the only way to obtain quantitative results which properly connect early and late time behavior. In this letter, we report the results of such a calculation, and examine the evolution of the post-collision stress-energy tensor.Unlike previous work considering singular shocks with vanishing thickness [5,9], or shocks driven by nonvanishing sources in the bulk [5,6], we choose to study planar gravitational "shocks" which are regular, nonsingular, source-less solutions to Einstein's equations. Equivalently, we study the evolution of initial states in SYM with finite energy density concentrated on two planar sheets of finite thickness (and Gaussian profile), propagating toward each other at the speed of light. The dual description only involves gravity in asymptotically AdS 5 spacetime; the complementary 5D internal manifold plays no role and may be ignored. Consequently, our results apply to all strongly coupled 4D conformal gauge theories with a pure gravitational dual description.

A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.

Using gauge/gravity duality, we study the creation and evolution of boost invariant anisotropic, strongly coupled N = 4 supersymmetric Yang-Mills plasma. In the dual gravitational description, this corresponds to horizon formation in a geometry driven to be anisotropic by a time-dependent change in boundary conditions.

We compute the penetration depth of a light quark moving through a large Nc, strongly coupled N = 4 supersymmetric Yang-Mills plasma using gauge/gravity duality and a combination of analytic and numerical techniques. We find that the maximum distance a quark with energy E can travel through a plasma is given by ∆xmax(E) = (C/T ) (E/T √ λ) 1/3 with C ≈ 0.5.