Conference

I will describe numerical simulations of quenches in AdS-CMT superconductors  where we are able to construct a dynamical phase diagram for the system. I will describe how the late time behaviour is
understood in terms of the quasinormal modes of the system, and how a rather generic behaviour of the pole structure there leads to interesting physical consequences that have an analog in condensed matter calculations using integrable models.

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.

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.