Holographic Batteries

Black holes play a central role in our understanding of gauge/gravity duality. They are often used to learn new properties about hot phases (in many cases, desconfined phases) of strongly coupled matter. However, we will argue that much can be learned about black holes by inspecting generic properties of gauge theories. For example, if we put two or more charge sources in contact with a field theory that possess charge carriers, a non-constant electric field develops. One way of achieving this scenario in gauge/gravity duality, is to consider two black holes at the boundary of AdS, with each of the black holes having different charges. If these two black holes connect through a common horizon in the bulk, the horizon will have a non-constant electric field, which seems at odds with rigidity theorems established in the seventies. Of course, these theorems assume that horizons are compact, which is not the case here since the horizon extends to the boundary. The aim of this project is to construct and study such solutions through the use of numerical methods, and measure for the first time nonlinear conductivities of strongly coupled matter.