Black holes in the limit of very many dimensions

General Relativity encompasses a huge variety of physical phenomena, from the collision of astrophysical black holes, to the dynamics (via holography) of strongly-coupled plasmas and the spontaneous symmetry-breaking in superconductors. Black holes play a central role in all this. However, their equations are exceedingly hard to solve. The apparent lack of a generic tunable parameter that allows to solve the theory perturbatively (like the electric coupling constant in electrodynamics, or the rank of the gauge group in large-NYang-Mills theory) is arguably the single most important obstacle for generic efficient approaches to the physics of strong gravity and black holes. In General Relativity, one natural parameter suggests itself: the number of dimensions D. Recently we have demonstrated that the limit of large D is optimally tailored for the investigation of black holes, classical and potentially also quantum. We have derived a simple set of nonlinear equations that describe the dynamical evolution of black holes, strings and branes that efficiently capture a surprisingly large amount of black hole physics.