Exploring AdS/CFT Dualities in Dynamical Settings - 2012

We study the isotropization of a homogeneous, strongly coupled, non-Abelian plasma by means of its gravity dual. We compare the time evolution of a large number of initially anisotropic states as determined, on the one hand, by the full non-linear Einstein's equations and, on the other, by the Einstein's equations linearized around the final equilibrium state. The linear approximation works remarkably well even for states that exhibit large anisotropies. For example, it predicts with a 20% accuracy the isotropization time, which is of order 1/T, with T the final equilibrium temperature. We comment on possible extensions to less symmetric situations.

I will describe a new numerical effort to solve Einstein gravity in 5-dimensional asymptotically Anti de Sitter spacetimes (AdS). The motivation is the gauge/gravity duality of string theory, with application to scenarios that on the gravity side are described by dynamical, strong-field solutions. For example, it has been argued that certain properties of the quark-gluon plasma formed in heavy-ion collisions can be modeled by a conformal field theory, with the dual description on the gravity side provided by the collision of black holes. As a first step towards modeling such more general phenomena, we initially focus on spacetimes with SO(3) symmetry in the bulk; i.e., axisymmetric gravity, dual to states with spherical or special conformal symmetry on the boundary. For a first application we study quasi-normal ringdown of highly deformed black holes in the bulk. Even though the initial states are far from equilibrium, the boundary state is remarkably well described as a hydrodynamic flow from early times. The code is based on the generalized harmonic formulation of the field equations, and though this method has been shown to work well in many asymptotically flat scenarios, there are unique challenges that arise in obtaining regular, stable solutions in asymptotically AdS spacetimes. I will describe these challenges, and the way we have addressed them.

It is well known that superradiance can extract energy from a black hole and, in an asymptotically global AdS background, it drives the black hole unstable. The onset of superradiance also signals a bifurcation to a new family of AdS black holes in a phase diagram of stationary solutions. We construct non-linearly the hairy black holes, solitons and boson stars associated to scalar superradiance. We present both charged and rotating solutions with scalar hair. In the charged case, the structure of phase diagram varies considerably, depending on the charge of the condensate. In the rotating case, the hairy solutions give the first examples of black holes with only a Killing field: the black holes are neither stationary nor axisymmetric, but are invariant under a single Killing field which is tangent to the null generators of the horizon.
We discuss the role of these solutions in a full time evolution of the superradiant instability. We emphasize how scarce is our knowledge of the rotating superradiant instability endpoint, and that this instability will compete with the turbulent instability of AdS.

In the context of the possible existence of large extra dimensions, and also the context of the AdS-CFT correspondence, there has been much interest in black holes solutions in theories of gravity and matter that are exotic - they might live in spacetime dimension other than 4, or have exotic matter and boundary conditions. I will review the types of physics that are accessible by studying such exotic black holes, ranging from LHC phenomenology to potential applications to condensed matter physics (via the AdS-CFT correspondence). One common theme is that traditional analytic methods
to find solutions tend not to work when confronted with these more exotic solutions and instead we are increasingly forced to use numerical techniques. I will discuss a numerical approach to finding static and stationary solutions, and give some example applications. I will also show how dynamical numerical simulations in these exotic contexts are playing an increasingly important role.